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Deck 10: Rotation of a Rigid Object About a Fixed Axis
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Question
A wheel (radius = 0.20 m)is mounted on a frictionless,horizontal axis.A light cord wrapped around the wheel supports a 0.50-kg object,as shown in the figure.When released from rest the object falls with a downward acceleration of 5.0 m/s2.What is the moment of inertia of the wheel? 
A)0.023 kg⋅m2
B)0.027 kg⋅m2
C)0.016 kg⋅m2
D)0.019 kg⋅m2
E)0.032 kg⋅m2
A)0.023 kg⋅m2
B)0.027 kg⋅m2
C)0.016 kg⋅m2
D)0.019 kg⋅m2
E)0.032 kg⋅m2
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A mass (M1 = 5.0 kg)is connected by a light cord to a mass (M2 = 4.0 kg)which slides on a smooth surface,as shown in the figure.The pulley (radius = 0.20 m)rotates about a frictionless axle.The acceleration of M2 is 3.5 m/s2.What is the moment of inertia of the pulley? 
A)0.29 kg⋅m2
B)0.42 kg⋅m2
C)0.20 kg⋅m2
D)0.62 kg⋅m2
E)0.60 kg⋅m2
A)0.29 kg⋅m2
B)0.42 kg⋅m2
C)0.20 kg⋅m2
D)0.62 kg⋅m2
E)0.60 kg⋅m2
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A wheel (radius = 0.25 m)is mounted on a frictionless,horizontal axis.The moment of inertia of the wheel about the axis is 0.040 kg⋅m2.A light cord wrapped around the wheel supports a 0.50-kg object as shown in the figure.The object is released from rest.What is the magnitude of the acceleration of the 0.50-kg object? 
A)3.0 m/s2
B)3.4 m/s2
C)4.3 m/s2
D)3.8 m/s2
E)2.7 m/s2
A)3.0 m/s2
B)3.4 m/s2
C)4.3 m/s2
D)3.8 m/s2
E)2.7 m/s2
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A mass m = 4.0 kg is connected,as shown,by a light cord to a mass M = 6.0 kg,which slides on a smooth horizontal surface.The pulley rotates about a frictionless axle and has a radius R = 0.12 m and a moment of inertia I = 0.090 kg⋅m2.The cord does not slip on the pulley.What is the magnitude of the acceleration of m? 
A)2.4 m/s2
B)2.8 m/s2
C)3.2 m/s2
D)4.2 m/s2
E)1.7 m/s2
A)2.4 m/s2
B)2.8 m/s2
C)3.2 m/s2
D)4.2 m/s2
E)1.7 m/s2
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A uniform rod of mass M = 1.2 kg and length L = 0.80 m,lying on a frictionless horizontal plane,is free to pivot about a vertical axis through one end,as shown.The moment of inertia of the rod about this axis is given by (1/3)ML2.If a force (F = 5.0 N,θ = 40°)acts as shown,what is the resulting angular acceleration about the pivot point? 
A)16 rad/s2
B)12 rad/s2
C)14 rad/s2
D)10 rad/s2
E)33 rad/s2
A)16 rad/s2
B)12 rad/s2
C)14 rad/s2
D)10 rad/s2
E)33 rad/s2
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The rigid object shown is rotated about an axis perpendicular to the paper and through point P.The total kinetic energy of the object as it rotates is equal to 1.4 J.If M = 1.3 kg and L = 0.50 m,what is the angular velocity of the object? Neglect the mass of the connecting rods and treat the masses as particles. 
A)1.3 rad/s
B)1.5 rad/s
C)1.7 rad/s
D)1.2 rad/s
E)2.1 rad/s
A)1.3 rad/s
B)1.5 rad/s
C)1.7 rad/s
D)1.2 rad/s
E)2.1 rad/s
Question
If M = 0.50 kg,L = 1.2 m,and the mass of each connecting rod shown is negligible,what is the moment of inertia about an axis perpendicular to the paper through the center of mass? Treat the mass as particles. 
A)3.7 kg⋅m2
B)2.8 kg⋅m2
C)3.2 kg⋅m2
D)2.3 kg⋅m2
E)3.9 kg⋅m2
A)3.7 kg⋅m2
B)2.8 kg⋅m2
C)3.2 kg⋅m2
D)2.3 kg⋅m2
E)3.9 kg⋅m2
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Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).
Refer to Exhibit 10-1.How many revolutions does she complete in the 16 minute period?
A)8
B)12
C)16
D)20
E)40
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).Refer to Exhibit 10-1.How many revolutions does she complete in the 16 minute period?
A)8
B)12
C)16
D)20
E)40
Question
Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
Refer to Exhibit 10-1.What is her angular displacement (in rad)in the first 12 minutes?
A)0
B)2π
C)4π
D)16π
E)32π
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).Refer to Exhibit 10-1.What is her angular displacement (in rad)in the first 12 minutes?
A)0
B)2π
C)4π
D)16π
E)32π
Question
Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
Refer to Exhibit 10-1.What is her angular displacement (in rad)in the 16 minute period shown in the graph?
A)0
B)16π
C)32π
D)40π
E)64π
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).Refer to Exhibit 10-1.What is her angular displacement (in rad)in the 16 minute period shown in the graph?
A)0
B)16π
C)32π
D)40π
E)64π
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Question
Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
The angular speed of the hour hand of a clock,in rad/s,is
A)
.
B)
.
C)
.
D)1 800π.
E)7 200π.
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).The angular speed of the hour hand of a clock,in rad/s,is
A)
.B)
.C)
.D)1 800π.
E)7 200π.
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Question
Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
Refer to Exhibit 10-1.How many revolutions does she complete in the first 12 minutes?
A)4
B)8
C)12
D)16
E)32
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).Refer to Exhibit 10-1.How many revolutions does she complete in the first 12 minutes?
A)4
B)8
C)12
D)16
E)32
Question
Two people are on a ride where the inside cars rotate at constant angular velocity three times the constant angular velocity of the outer cars.If the two cars are in line at t = 0,and moving at 3ω and ω respectively,at what time will they next pass each other?
A)t = 0.
B)t =
.
C)t =
.
D)t =
.
E)t =
.
A)t = 0.
B)t =
.C)t =
.D)t =
.E)t =
. Question
Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
A uniform cylinder of radius R,mass M,and length L rotates freely about a horizontal axis parallel and tangent to the cylinder,as shown below.The moment of inertia of the cylinder about this axis is
A)
.
B)
.
C)MR2.
D)
.
E)
.
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).A uniform cylinder of radius R,mass M,and length L rotates freely about a horizontal axis parallel and tangent to the cylinder,as shown below.The moment of inertia of the cylinder about this axis is
A)
.B)
.C)MR2.
D)
.E)
. Question
The graphs below show angular velocity as a function of time.In which one is the magnitude of the angular acceleration constantly decreasing?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
The angular speed of the minute hand of a clock,in rad/s,is
A)
.
B)
.
C)
.
D)π.
E)120π.
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).The angular speed of the minute hand of a clock,in rad/s,is
A)
.B)
.C)
.D)π.
E)120π.
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Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
Refer to Exhibit 10-1.What is her angular displacement (in rad)in the first 8 minutes?
A)0
B)π
C)4π
D)8π
E)16π
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).Refer to Exhibit 10-1.What is her angular displacement (in rad)in the first 8 minutes?
A)0
B)π
C)4π
D)8π
E)16π
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The rigid body shown is rotated about an axis perpendicular to the paper and through the point P.If M = 0.40 kg,a = 30 cm,and b = 50 cm,how much work is required to take the body from rest to an angular speed of 5.0 rad/s? Neglect the mass of the connecting rods and treat the masses as particles. 
A)2.9 J
B)2.6 J
C)3.1 J
D)3.4 J
E)1.6 J
A)2.9 J
B)2.6 J
C)3.1 J
D)3.4 J
E)1.6 J
Question
Two forces of magnitude 50 N,as shown in the figure below,act on a cylinder of radius 4 m and mass 6.25 kg.The cylinder,which is initially at rest,sits on a frictionless surface.After 1 second,the velocity and angular velocity of the cylinder in m/s and rad/s are respectively 
A)v = 0;ω = 0.
B)v = 0;ω = 4.
C)v = 0;ω = 8.
D)v = 8;ω = 8.
E)v = 16;ω = 8.
A)v = 0;ω = 0.
B)v = 0;ω = 4.
C)v = 0;ω = 8.
D)v = 8;ω = 8.
E)v = 16;ω = 8.
Question
The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track.Through how many radians does the car travel in the first 10 minutes? 
A)30
B)50
C)70
D)90
E)100
A)30
B)50
C)70
D)90
E)100
Question
The rigid body shown rotates about an axis through its center of mass and perpendicular to the paper.If M = 2.0 kg and L = 80 cm,what is the kinetic energy of this object when its angular speed about this axis is equal to 5.0 rad/s? Neglect the mass of the connecting rod and treat the masses as particles. 
A)18 J
B)15 J
C)12 J
D)23 J
E)26 J
A)18 J
B)15 J
C)12 J
D)23 J
E)26 J
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Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
A uniform sphere of radius R and mass M rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere,as shown below.The moment of inertia of the sphere about this axis is
A)
.
B)
.
C)
.
D)
.
E)
.
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).A uniform sphere of radius R and mass M rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere,as shown below.The moment of inertia of the sphere about this axis is
A)
.B)
.C)
.D)
.E)
. Question
Exhibit 10-2
The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track.
Use this exhibit to answer the following question(s).
Refer to Exhibit 10-2.What is his average angular acceleration,in rad/s2,in the period from t = 6 min to t = 8 min?
A)0
B)
C)
D)
E)
The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track.
Use this exhibit to answer the following question(s).Refer to Exhibit 10-2.What is his average angular acceleration,in rad/s2,in the period from t = 6 min to t = 8 min?
A)0
B)
C)
D)
E)
Question
Exhibit 10-3
The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s.
Use this exhibit to answer the following question(s).
Refer to Exhibit 10-3.The angular position,θ,at t = 0 s is 3.0 rad,clockwise.The angular position,θ,at t = 7 s is
A)27 rad,CW.
B)27 rad,CCW.
C)33 rad,CW.
D)33 rad,CCW.
E)36 rad,CCW.
The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s.
Use this exhibit to answer the following question(s).Refer to Exhibit 10-3.The angular position,θ,at t = 0 s is 3.0 rad,clockwise.The angular position,θ,at t = 7 s is
A)27 rad,CW.
B)27 rad,CCW.
C)33 rad,CW.
D)33 rad,CCW.
E)36 rad,CCW.
Question
Exhibit 10-3
The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s. Use this exhibit to answer the following question(s).
Refer to Exhibit 10-3.The change in angular position,Δθ,during the 7-second period is
A)21 rad,CW.
B)21 rad,CCW.
C)30 rad,CW.
D)30 rad,CCW.
E)39 rad,CCW.
The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s.
Use this exhibit to answer the following question(s).Refer to Exhibit 10-3.The change in angular position,Δθ,during the 7-second period is
A)21 rad,CW.
B)21 rad,CCW.
C)30 rad,CW.
D)30 rad,CCW.
E)39 rad,CCW.
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When the center of a bicycle wheel has linear velocity 
Relative to the ground,the velocity relative to the ground of point P' at the top of the wheel is
A)0.
B)
.
C)
.
D)
.
E)
.
Relative to the ground,the velocity relative to the ground of point P' at the top of the wheel is
A)0.
B)
.C)
.D)
.E)
. Question
Question
Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
The angular speed of the hour hand of a clock,in rad/min,is
A)
.
B)
.
C)
.
D)π.
E)120π.
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).The angular speed of the hour hand of a clock,in rad/min,is
A)
.B)
.C)
.D)π.
E)120π.
Question
The graph below shows a plot of angular acceleration in rad/s2 versus time from t = 0 s to t = 8 s.The change in angular velocity,Δω,during this 8-second period is 
A)
,CW.
B)
,CCW.
C)
,CW.
D)
,CCW.
E)
,CW.
A)
,CW.B)
,CCW.C)
,CW.D)
,CCW.E)
,CW. Question
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Which of the following diagrams shows the greatest magnitude net torque with a zero net force? All the rods,of length 2r,rotate about an axis that is perpendicular to the rod and fixed in the center of the rod.All the forces are of magnitude F or 2F and all distances from the axis are r or r/2.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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The graph below shows a plot of angular acceleration in rad/s2 versus time from t = 0 s to t = 8 s.The angular velocity at t = 0 s is 
,CCW.The angular velocity,ω,at t = 8 s is
A)
,CW.
B)
,CCW.
C)
,CW.
D)
,CCW.
E)
,CW.
,CCW.The angular velocity,ω,at t = 8 s is
A)
,CW.B)
,CCW.C)
,CW.D)
,CCW.E)
,CW. Question
Question
Exhibit 10-2
The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track. Use this exhibit to answer the following question(s).
Refer to Exhibit 10-2.What is his average angular acceleration,in rad/s2,in the first 10 minutes?
A)0
B)
C)
D)
E)
The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track.
Use this exhibit to answer the following question(s).Refer to Exhibit 10-2.What is his average angular acceleration,in rad/s2,in the first 10 minutes?
A)0
B)
C)
D)
E)
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Question
Question
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Deck 10: Rotation of a Rigid Object About a Fixed Axis
1
A wheel (radius = 0.20 m)is mounted on a frictionless,horizontal axis.A light cord wrapped around the wheel supports a 0.50-kg object,as shown in the figure.When released from rest the object falls with a downward acceleration of 5.0 m/s2.What is the moment of inertia of the wheel?
A)0.023 kg⋅m2
B)0.027 kg⋅m2
C)0.016 kg⋅m2
D)0.019 kg⋅m2
E)0.032 kg⋅m2
A)0.023 kg⋅m2
B)0.027 kg⋅m2
C)0.016 kg⋅m2
D)0.019 kg⋅m2
E)0.032 kg⋅m2
0.019 kg⋅m2
2
At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration of −0.40 rad/s2 has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad.What is the angular position of the wheel at t = 2.0 s?
A)4.9 rad
B)4.7 rad
C)4.5 rad
D)4.3 rad
E)4.1 rad
A)4.9 rad
B)4.7 rad
C)4.5 rad
D)4.3 rad
E)4.1 rad
4.5 rad
3
A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s.During a 5.0-s interval the angular velocity decreases to 10 rad/s.Assume that the angular acceleration is constant during the 5.0-s interval.How many radians does the wheel turn through during the 5.0-s interval?
A)95 rad
B)85 rad
C)65 rad
D)75 rad
E)125 rad
A)95 rad
B)85 rad
C)65 rad
D)75 rad
E)125 rad
75 rad
4
A wheel (radius = 0.20 m)starts from rest and rotates with a constant angular acceleration of 2.0 rad/s2.At the instant when the angular velocity is equal to 1.2 rad/s,what is the magnitude of the total linear acceleration of a point on the rim of the wheel?
A)0.40 m/s2
B)0.29 m/s2
C)0.69 m/s2
D)0.49 m/s2
E)0.35 m/s2
A)0.40 m/s2
B)0.29 m/s2
C)0.69 m/s2
D)0.49 m/s2
E)0.35 m/s2
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5
A mass (M1 = 5.0 kg)is connected by a light cord to a mass (M2 = 4.0 kg)which slides on a smooth surface,as shown in the figure.The pulley (radius = 0.20 m)rotates about a frictionless axle.The acceleration of M2 is 3.5 m/s2.What is the moment of inertia of the pulley?
A)0.29 kg⋅m2
B)0.42 kg⋅m2
C)0.20 kg⋅m2
D)0.62 kg⋅m2
E)0.60 kg⋅m2
A)0.29 kg⋅m2
B)0.42 kg⋅m2
C)0.20 kg⋅m2
D)0.62 kg⋅m2
E)0.60 kg⋅m2
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6
A disk (radius = 8.0 cm)that rotates about a fixed axis starts from rest and accelerates at a constant rate to an angular velocity of 4.0 rad/s in 2.0 s.What is the magnitude of the total linear acceleration of a point on the rim of the disk at the instant when the angular velocity of the disk is 1.5 rad/s?
A)24 cm/s2
B)16 cm/s2
C)18 cm/s2
D)34 cm/s2
E)44 cm/s2
A)24 cm/s2
B)16 cm/s2
C)18 cm/s2
D)34 cm/s2
E)44 cm/s2
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7
A horizontal disk with a radius of 10 cm rotates about a vertical axis through its center.The disk starts from rest at t = 0 and has a constant angular acceleration of 2.1 rad/s2.At what value of t will the radial and tangential components of the linear acceleration of a point on the rim of the disk be equal in magnitude?
A)0.55 s
B)0.63 s
C)0.69 s
D)0.59 s
E)0.47 s
A)0.55 s
B)0.63 s
C)0.69 s
D)0.59 s
E)0.47 s
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8
A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s2 starts from rest at t = 0.The wheel has a diameter of 20 cm.What is the magnitude of the total linear acceleration of a point on the outer edge of the wheel at t = 0.60 s?
A)0.25 m/s2
B)0.50 m/s2
C)0.14 m/s2
D)0.34 m/s2
E)0.20 m/s2
A)0.25 m/s2
B)0.50 m/s2
C)0.14 m/s2
D)0.34 m/s2
E)0.20 m/s2
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9
A wheel (radius = 0.25 m)is mounted on a frictionless,horizontal axis.The moment of inertia of the wheel about the axis is 0.040 kg⋅m2.A light cord wrapped around the wheel supports a 0.50-kg object as shown in the figure.The object is released from rest.What is the magnitude of the acceleration of the 0.50-kg object?
A)3.0 m/s2
B)3.4 m/s2
C)4.3 m/s2
D)3.8 m/s2
E)2.7 m/s2
A)3.0 m/s2
B)3.4 m/s2
C)4.3 m/s2
D)3.8 m/s2
E)2.7 m/s2
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10
At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.0 rad/s.Two seconds later it has turned through 5.0 complete revolutions.What is the angular acceleration of this wheel?
A)17 rad/s2
B)14 rad/s2
C)20 rad/s2
D)23 rad/s2
E)13 rad/s2
A)17 rad/s2
B)14 rad/s2
C)20 rad/s2
D)23 rad/s2
E)13 rad/s2
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11
A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s2 turns through 2.4 revolutions during a 2.0-s time interval.What is the angular velocity at the end of this time interval?
A)9.5 rad/s
B)9.7 rad/s
C)9.3 rad/s
D)9.1 rad/s
E)8.8 rad/s
A)9.5 rad/s
B)9.7 rad/s
C)9.3 rad/s
D)9.1 rad/s
E)8.8 rad/s
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12
The turntable of a record player has an angular velocity of 8.0 rad/s when it is turned off.The turntable comes to rest 2.5 s after being turned off.Through how many radians does the turntable rotate after being turned off? Assume constant angular acceleration.
A)12 rad
B)8.0 rad
C)10 rad
D)16 rad
E)6.8 rad
A)12 rad
B)8.0 rad
C)10 rad
D)16 rad
E)6.8 rad
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13
A cylinder rotating about its axis with a constant angular acceleration of 1.6 rad/s2 starts from rest at t = 0.At the instant when it has turned through 0.40 radian,what is the magnitude of the total linear acceleration of a point on the rim (radius = 13 cm)?
A)0.31 m/s2
B)0.27 m/s2
C)0.35 m/s2
D)0.39 m/s2
E)0.45 m/s2
A)0.31 m/s2
B)0.27 m/s2
C)0.35 m/s2
D)0.39 m/s2
E)0.45 m/s2
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14
A wheel rotating about a fixed axis has a constant angular acceleration of 4.0 rad/s2.In a 4.0-s interval the wheel turns through an angle of 80 radians.Assuming the wheel started from rest,how long had it been in motion at the start of the 4.0-s interval?
A)2.5 s
B)4.0 s
C)3.5 s
D)3.0 s
E)4.5 s
A)2.5 s
B)4.0 s
C)3.5 s
D)3.0 s
E)4.5 s
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15
A thin uniform rod (length = 1.2 m,mass = 2.0 kg)is pivoted about a horizontal,frictionless pin through one end of the rod.(The moment of inertia of the rod about this axis is ML2/3. )The rod is released when it makes an angle of 37° with the horizontal.What is the angular acceleration of the rod at the instant it is released?
A)9.8 rad/s2
B)7.4 rad/s2
C)8.4 rad/s2
D)5.9 rad/s2
E)6.5 rad/s2
A)9.8 rad/s2
B)7.4 rad/s2
C)8.4 rad/s2
D)5.9 rad/s2
E)6.5 rad/s2
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16
A mass m = 4.0 kg is connected,as shown,by a light cord to a mass M = 6.0 kg,which slides on a smooth horizontal surface.The pulley rotates about a frictionless axle and has a radius R = 0.12 m and a moment of inertia I = 0.090 kg⋅m2.The cord does not slip on the pulley.What is the magnitude of the acceleration of m?
A)2.4 m/s2
B)2.8 m/s2
C)3.2 m/s2
D)4.2 m/s2
E)1.7 m/s2
A)2.4 m/s2
B)2.8 m/s2
C)3.2 m/s2
D)4.2 m/s2
E)1.7 m/s2
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17
A wheel rotates about a fixed axis with a constant angular acceleration of 4.0 rad/s2.The diameter of the wheel is 40 cm.What is the linear speed of a point on the rim of this wheel at an instant when that point has a total linear acceleration with a magnitude of 1.2 m/s2?
A)39 cm/s
B)42 cm/s
C)45 cm/s
D)35 cm/s
E)53 cm/s
A)39 cm/s
B)42 cm/s
C)45 cm/s
D)35 cm/s
E)53 cm/s
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18
A wheel starts from rest and rotates with a constant angular acceleration about a fixed axis.It completes the first revolution 6.0 s after it started.How long after it started will the wheel complete the second revolution?
A)9.9 s
B)7.8 s
C)8.5 s
D)9.2 s
E)6.4 s
A)9.9 s
B)7.8 s
C)8.5 s
D)9.2 s
E)6.4 s
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19
A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s.During a 5.0-s interval the angular velocity increases to 40 rad/s.Assume that the angular acceleration was constant during the 5.0-s interval.How many revolutions does the wheel turn through during the 5.0-s interval?
A)20 rev
B)24 rev
C)32 rev
D)28 rev
E)39 rev
A)20 rev
B)24 rev
C)32 rev
D)28 rev
E)39 rev
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20
A wheel rotating about a fixed axis has an angular position given by θ = 3.0 − 2.0t3,where θ is measured in radians and t in seconds.What is the angular acceleration of the wheel at t = 2.0 s?
A)−1.0 rad/s2
B)−24 rad/s2
C)−2.0 rad/s2
D)−4.0 rad/s2
E)−3.5 rad/s2
A)−1.0 rad/s2
B)−24 rad/s2
C)−2.0 rad/s2
D)−4.0 rad/s2
E)−3.5 rad/s2
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21
Four identical particles (mass of each = 0.40 kg)are placed at the vertices of a rectangle (2.0 m × 3.0 m)and held in those positions by four light rods which form the sides of the rectangle.What is the moment of inertia of this rigid body about an axis that passes through the mid-points of the longer sides and is parallel to the shorter sides?
A)2.7 kg⋅m2
B)3.6 kg⋅m2
C)3.1 kg⋅m2
D)4.1 kg⋅m2
E)1.6 kg⋅m2
A)2.7 kg⋅m2
B)3.6 kg⋅m2
C)3.1 kg⋅m2
D)4.1 kg⋅m2
E)1.6 kg⋅m2
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22
A wheel (radius = 12 cm)is mounted on a frictionless,horizontal axle that is perpendicular to the wheel and passes through the center of mass of the wheel.A light cord wrapped around the wheel supports a 0.40-kg object.If released from rest with the string taut,the object is observed to fall with a downward acceleration of 3.0 m/s2.What is the moment of inertia (of the wheel)about the given axle?
A)0.023 kg⋅m2
B)0.013 kg⋅m2
C)0.020 kg⋅m2
D)0.016 kg⋅m2
E)0.035 kg⋅m2
A)0.023 kg⋅m2
B)0.013 kg⋅m2
C)0.020 kg⋅m2
D)0.016 kg⋅m2
E)0.035 kg⋅m2
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23
Two particles (m1 = 0.20 kg,m2 = 0.30 kg)are positioned at the ends of a 2.0-m long rod of negligible mass.What is the moment of inertia of this rigid body about an axis perpendicular to the rod and through the center of mass?
A)0.48 kg⋅m2
B)0.50 kg⋅m2
C)1.2 kg⋅m2
D)0.80 kg⋅m2
E)0.70 kg⋅m2
A)0.48 kg⋅m2
B)0.50 kg⋅m2
C)1.2 kg⋅m2
D)0.80 kg⋅m2
E)0.70 kg⋅m2
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24
A uniform rod is 2.0 m long.The rod is pivoted about a horizontal,frictionless pin through one end.The rod is released from rest at the horizontal position.What is the angular acceleration of the rod at the instant the rod makes an angle of 70° with the horizontal?
A)3.7 rad/s2
B)1.3 rad/s2
C)2.5 rad/s2
D)4.9 rad/s2
E)1.9 rad/s2
A)3.7 rad/s2
B)1.3 rad/s2
C)2.5 rad/s2
D)4.9 rad/s2
E)1.9 rad/s2
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25
A uniform meter stick is pivoted to rotate about a horizontal axis through the 25-cm mark on the stick.The stick is released from rest in a horizontal position.The moment of inertia of a uniform rod about an axis perpendicular to the rod and through the center of mass of the rod is given by (1/12)ML2.Determine the magnitude of the initial angular acceleration of the stick.
A)17 rad/s2
B)13 rad/s2
C)15 rad/s2
D)19 rad/s2
E)23 rad/s2
A)17 rad/s2
B)13 rad/s2
C)15 rad/s2
D)19 rad/s2
E)23 rad/s2
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26
Identical particles are placed at the 50-cm and 80-cm marks on a meter stick of negligible mass.This rigid body is then mounted so as to rotate freely about a pivot at the 0-cm mark on the meter stick.If this body is released from rest in a horizontal position,what is the angular speed of the meter stick as it swings through its lowest position?
A)4.2 rad/s
B)5.4 rad/s
C)4.6 rad/s
D)5.0 rad/s
E)1.7 rad/s
A)4.2 rad/s
B)5.4 rad/s
C)4.6 rad/s
D)5.0 rad/s
E)1.7 rad/s
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27
A uniform rod (mass = 1.5 kg)is 2.0 m long.The rod is pivoted about a horizontal,frictionless pin through one end.The rod is released from rest in a horizontal position.What is the angular speed of the rod when the rod makes an angle of 30° with the horizontal? (The moment of inertia of the rod about the pin is 2.0 kg⋅m2).
A)2.2 rad/s
B)3.6 rad/s
C)2.7 rad/s
D)3.1 rad/s
E)1.8 rad/s
A)2.2 rad/s
B)3.6 rad/s
C)2.7 rad/s
D)3.1 rad/s
E)1.8 rad/s
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28
Particles (mass of each = 0.20 kg)are placed at the 40-cm and 100-cm marks of a meter stick of negligible mass.This rigid body is free to rotate about a frictionless pivot at the 0-cm end.The body is released from rest in the horizontal position.What is the initial angular acceleration of the body?
A)12 rad/s2
B)5.9 rad/s2
C)8.4 rad/s2
D)5.4 rad/s2
E)17 rad/s2
A)12 rad/s2
B)5.9 rad/s2
C)8.4 rad/s2
D)5.4 rad/s2
E)17 rad/s2
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29
A uniform rod of mass M = 1.2 kg and length L = 0.80 m,lying on a frictionless horizontal plane,is free to pivot about a vertical axis through one end,as shown.The moment of inertia of the rod about this axis is given by (1/3)ML2.If a force (F = 5.0 N,θ = 40°)acts as shown,what is the resulting angular acceleration about the pivot point?
A)16 rad/s2
B)12 rad/s2
C)14 rad/s2
D)10 rad/s2
E)33 rad/s2
A)16 rad/s2
B)12 rad/s2
C)14 rad/s2
D)10 rad/s2
E)33 rad/s2
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30
A uniform rod is 3.0 m long.The rod is pivoted about a horizontal,frictionless pin through one end.The rod is released from rest at an angle of 27° above the horizontal.What is the angular speed of the rod as it passes through the horizontal position?
A)3.0 rad/s
B)2.8 rad/s
C)2.1 rad/s
D)2.5 rad/s
E)3.4 rad/s
A)3.0 rad/s
B)2.8 rad/s
C)2.1 rad/s
D)2.5 rad/s
E)3.4 rad/s
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31
A uniform rod is 2.0 m long.The rod is pivoted about a horizontal,frictionless pin through one end.The rod is released from rest at an angle of 30° above the horizontal.What is the angular acceleration of the rod at the instant it is released?
A)4.7 rad/s2
B)6.9 rad/s2
C)6.4 rad/s2
D)5.6 rad/s2
E)4.2 rad/s2
A)4.7 rad/s2
B)6.9 rad/s2
C)6.4 rad/s2
D)5.6 rad/s2
E)4.2 rad/s2
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32
The rigid object shown is rotated about an axis perpendicular to the paper and through point P.The total kinetic energy of the object as it rotates is equal to 1.4 J.If M = 1.3 kg and L = 0.50 m,what is the angular velocity of the object? Neglect the mass of the connecting rods and treat the masses as particles.
A)1.3 rad/s
B)1.5 rad/s
C)1.7 rad/s
D)1.2 rad/s
E)2.1 rad/s
A)1.3 rad/s
B)1.5 rad/s
C)1.7 rad/s
D)1.2 rad/s
E)2.1 rad/s
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33
If M = 0.50 kg,L = 1.2 m,and the mass of each connecting rod shown is negligible,what is the moment of inertia about an axis perpendicular to the paper through the center of mass? Treat the mass as particles.
A)3.7 kg⋅m2
B)2.8 kg⋅m2
C)3.2 kg⋅m2
D)2.3 kg⋅m2
E)3.9 kg⋅m2
A)3.7 kg⋅m2
B)2.8 kg⋅m2
C)3.2 kg⋅m2
D)2.3 kg⋅m2
E)3.9 kg⋅m2
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34
A uniform rod (length = 2.0 m)is mounted to rotate freely about a horizontal axis that is perpendicular to the rod and that passes through the rod at a point 0.50 m from one end of the rod.If the rod is released from rest in a horizontal position,what is the angular speed of the rod as it rotates through its lowest position?
A)3.5 rad/s
B)3.8 rad/s
C)4.1 rad/s
D)2.0 rad/s
E)5.6 rad/s
A)3.5 rad/s
B)3.8 rad/s
C)4.1 rad/s
D)2.0 rad/s
E)5.6 rad/s
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35
A uniform rod (mass = 2.0 kg,length = 0.60 m)is free to rotate about a frictionless pivot at one end.The rod is released from rest in the horizontal position.What is the magnitude of the angular acceleration of the rod at the instant it is 60° below the horizontal?
A)15 rad/s2
B)12 rad/s2
C)18 rad/s2
D)29 rad/s2
E)23 rad/s2
A)15 rad/s2
B)12 rad/s2
C)18 rad/s2
D)29 rad/s2
E)23 rad/s2
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36
Particles (mass of each = 0.40 kg)are placed at the 60-cm and 100-cm marks of a meter stick of negligible mass.This rigid body is free to rotate about a frictionless pivot at the 0-cm end.The body is released from rest in the horizontal position.What is the magnitude of the initial linear acceleration of the end of the body opposite the pivot?
A)15 m/s2
B)9.8 m/s2
C)5.8 m/s2
D)12 m/s2
E)4.7 m/s2
A)15 m/s2
B)9.8 m/s2
C)5.8 m/s2
D)12 m/s2
E)4.7 m/s2
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37
Four identical particles (mass of each = 0.40 kg)are placed at the vertices of a rectangle (2.5 m × 4.0 m)and held in those positions by four light rods which form the sides of the rectangle.What is the moment of inertia of this rigid body about an axis that passes through the mid-points of the shorter sides and is parallel to the longer sides?
A)2.2 kg⋅m2
B)2.8 kg⋅m2
C)2.5 kg⋅m2
D)3.1 kg⋅m2
E)1.6 kg⋅m2
A)2.2 kg⋅m2
B)2.8 kg⋅m2
C)2.5 kg⋅m2
D)3.1 kg⋅m2
E)1.6 kg⋅m2
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38
Four identical particles (mass of each = 0.24 kg)are placed at the vertices of a rectangle (2.0 m × 3.0 m)and held in those positions by four light rods which form the sides of the rectangle.What is the moment of inertia of this rigid body about an axis that passes through the center of mass of the body and is parallel to the shorter sides of the rectangle?
A)2.4 kg⋅m2
B)2.2 kg⋅m2
C)1.9 kg⋅m2
D)2.7 kg⋅m2
E)8.6 kg⋅m2
A)2.4 kg⋅m2
B)2.2 kg⋅m2
C)1.9 kg⋅m2
D)2.7 kg⋅m2
E)8.6 kg⋅m2
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39
A uniform rod of length (L = 2.0 m)and mass (M = 1.5 kg)is pivoted about a horizontal frictionless pin through one end.The rod is released from rest at an angle of 30° below the horizontal.What is the angular speed of the rod when it passes through the vertical position? (The moment of inertia of the rod about the pin is 2.0 kg⋅m2. )
A)3.5 rad/s
B)2.7 rad/s
C)3.1 rad/s
D)2.3 rad/s
E)1.6 rad/s
A)3.5 rad/s
B)2.7 rad/s
C)3.1 rad/s
D)2.3 rad/s
E)1.6 rad/s
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40
Three particles,each of which has a mass of 80 g,are positioned at the vertices of an equilateral triangle with sides of length 60 cm.The particles are connected by rods of negligible mass.What is the moment of inertia of this rigid body about an axis that is parallel to one side of the triangle and passes through the respective midpoints of the other two sides?
A)0.018 kg⋅m2
B)0.020 kg⋅m2
C)0.016 kg⋅m2
D)0.022 kg⋅m2
E)0.032 kg⋅m2
A)0.018 kg⋅m2
B)0.020 kg⋅m2
C)0.016 kg⋅m2
D)0.022 kg⋅m2
E)0.032 kg⋅m2
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41
A nonuniform 2.0-kg rod is 2.0 m long.The rod is mounted to rotate freely about a horizontal axis perpendicular to the rod that passes through one end of the rod.The moment of inertia of the rod about this axis is 4.0 kg⋅m2.The center of mass of the rod is 1.2 m from the axis.If the rod is released from rest in the horizontal position,what is its angular speed as it swings through the vertical position?
A)3.4 rad/s
B)4.4 rad/s
C)4.3 rad/s
D)5.8 rad/s
E)6.8 rad/s
A)3.4 rad/s
B)4.4 rad/s
C)4.3 rad/s
D)5.8 rad/s
E)6.8 rad/s
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42
Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
Refer to Exhibit 10-1.How many revolutions does she complete in the 16 minute period?
A)8
B)12
C)16
D)20
E)40
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).Refer to Exhibit 10-1.How many revolutions does she complete in the 16 minute period?
A)8
B)12
C)16
D)20
E)40
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43
Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
Refer to Exhibit 10-1.What is her angular displacement (in rad)in the first 12 minutes?
A)0
B)2π
C)4π
D)16π
E)32π
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).Refer to Exhibit 10-1.What is her angular displacement (in rad)in the first 12 minutes?
A)0
B)2π
C)4π
D)16π
E)32π
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44
Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
Refer to Exhibit 10-1.What is her angular displacement (in rad)in the 16 minute period shown in the graph?
A)0
B)16π
C)32π
D)40π
E)64π
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).Refer to Exhibit 10-1.What is her angular displacement (in rad)in the 16 minute period shown in the graph?
A)0
B)16π
C)32π
D)40π
E)64π
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45
You throw a Frisbee of mass m and radius r so that it is spinning about a horizontal axis perpendicular to the plane of the Frisbee.Ignoring air resistance,the torque exerted about its center of mass by gravity is
A)0.
B)mgr.
C)2mgr.
D)a function of the angular velocity.
E)small at first,then increasing as the Frisbee loses the torque given it by your hand.
A)0.
B)mgr.
C)2mgr.
D)a function of the angular velocity.
E)small at first,then increasing as the Frisbee loses the torque given it by your hand.
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46
Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
The angular speed of the hour hand of a clock,in rad/s,is
A) .
B) .
C) .
D)1 800π.
E)7 200π.
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).The angular speed of the hour hand of a clock,in rad/s,is
A)
.B)
.C)
.D)1 800π.
E)7 200π.
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47
Two cylinders made of the same material roll down a plane inclined at an angle θ with the horizontal.Each travels the same distance.The radius of cylinder B is twice the radius of cylinder A.In what order do they reach the bottom?
A)A reaches the bottom first because it has the greater acceleration.
B)A reaches the bottom first because it has a smaller moment of inertia.
C)B reaches the bottom first because is experiences a larger torque.
D)B reaches the bottom first because it travels a larger distance in one rotation.
E)They both reach the bottom at the same time,because each has the same linear acceleration.
A)A reaches the bottom first because it has the greater acceleration.
B)A reaches the bottom first because it has a smaller moment of inertia.
C)B reaches the bottom first because is experiences a larger torque.
D)B reaches the bottom first because it travels a larger distance in one rotation.
E)They both reach the bottom at the same time,because each has the same linear acceleration.
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48
Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
Refer to Exhibit 10-1.How many revolutions does she complete in the first 12 minutes?
A)4
B)8
C)12
D)16
E)32
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).Refer to Exhibit 10-1.How many revolutions does she complete in the first 12 minutes?
A)4
B)8
C)12
D)16
E)32
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49
Two people are on a ride where the inside cars rotate at constant angular velocity three times the constant angular velocity of the outer cars.If the two cars are in line at t = 0,and moving at 3ω and ω respectively,at what time will they next pass each other?
A)t = 0.
B)t = .
C)t = .
D)t = .
E)t = .
A)t = 0.
B)t =
.C)t =
.D)t =
.E)t =
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50
Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
A uniform cylinder of radius R,mass M,and length L rotates freely about a horizontal axis parallel and tangent to the cylinder,as shown below.The moment of inertia of the cylinder about this axis is
A) .
B) .
C)MR2.
D) .
E) .
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).A uniform cylinder of radius R,mass M,and length L rotates freely about a horizontal axis parallel and tangent to the cylinder,as shown below.The moment of inertia of the cylinder about this axis is
A)
.B)
.C)MR2.
D)
.E)
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51
The graphs below show angular velocity as a function of time.In which one is the magnitude of the angular acceleration constantly decreasing?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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52
Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
The angular speed of the minute hand of a clock,in rad/s,is
A) .
B) .
C) .
D)π.
E)120π.
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).The angular speed of the minute hand of a clock,in rad/s,is
A)
.B)
.C)
.D)π.
E)120π.
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53
A campus bird spots a member of an opposing football team in an amusement park.The football player is on a ride where he goes around at angular velocity ω at distance R from the center.The bird flies in a horizontal circle above him.Will a dropping the bird releases while flying directly above the person's head hit him?
A)Yes,because it falls straight down.
B)Yes,because it maintains the acceleration of the bird as it falls.
C)No,because it falls straight down and will land behind the person.
D)Yes,because it maintains the angular velocity of the bird as it falls.
E)No,because it maintains the tangential velocity the bird had at the instant it started falling.
A)Yes,because it falls straight down.
B)Yes,because it maintains the acceleration of the bird as it falls.
C)No,because it falls straight down and will land behind the person.
D)Yes,because it maintains the angular velocity of the bird as it falls.
E)No,because it maintains the tangential velocity the bird had at the instant it started falling.
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54
Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
Refer to Exhibit 10-1.What is her angular displacement (in rad)in the first 8 minutes?
A)0
B)π
C)4π
D)8π
E)16π
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).Refer to Exhibit 10-1.What is her angular displacement (in rad)in the first 8 minutes?
A)0
B)π
C)4π
D)8π
E)16π
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55
A uniform rod (length = 2.4 m)of negligible mass has a 1.0-kg point mass attached to one end and a 2.0-kg point mass attached to the other end.The rod is mounted to rotate freely about a horizontal axis that is perpendicular to the rod and that passes through a point 1.0 m from the 2.0-kg mass.The rod is released from rest when it is horizontal.What is the angular velocity of the rod at the instant the 2.0-kg mass passes through its low point?
A)1.7 rad/s
B)2.2 rad/s
C)2.0 rad/s
D)1.5 rad/s
E)3.1 rad/s
A)1.7 rad/s
B)2.2 rad/s
C)2.0 rad/s
D)1.5 rad/s
E)3.1 rad/s
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56
The rigid body shown is rotated about an axis perpendicular to the paper and through the point P.If M = 0.40 kg,a = 30 cm,and b = 50 cm,how much work is required to take the body from rest to an angular speed of 5.0 rad/s? Neglect the mass of the connecting rods and treat the masses as particles.
A)2.9 J
B)2.6 J
C)3.1 J
D)3.4 J
E)1.6 J
A)2.9 J
B)2.6 J
C)3.1 J
D)3.4 J
E)1.6 J
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57
Two forces of magnitude 50 N,as shown in the figure below,act on a cylinder of radius 4 m and mass 6.25 kg.The cylinder,which is initially at rest,sits on a frictionless surface.After 1 second,the velocity and angular velocity of the cylinder in m/s and rad/s are respectively
A)v = 0;ω = 0.
B)v = 0;ω = 4.
C)v = 0;ω = 8.
D)v = 8;ω = 8.
E)v = 16;ω = 8.
A)v = 0;ω = 0.
B)v = 0;ω = 4.
C)v = 0;ω = 8.
D)v = 8;ω = 8.
E)v = 16;ω = 8.
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58
The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track.Through how many radians does the car travel in the first 10 minutes?
A)30
B)50
C)70
D)90
E)100
A)30
B)50
C)70
D)90
E)100
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59
The rigid body shown rotates about an axis through its center of mass and perpendicular to the paper.If M = 2.0 kg and L = 80 cm,what is the kinetic energy of this object when its angular speed about this axis is equal to 5.0 rad/s? Neglect the mass of the connecting rod and treat the masses as particles.
A)18 J
B)15 J
C)12 J
D)23 J
E)26 J
A)18 J
B)15 J
C)12 J
D)23 J
E)26 J
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60
Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
A uniform sphere of radius R and mass M rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere,as shown below.The moment of inertia of the sphere about this axis is
A) .
B) .
C) .
D) .
E) .
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).A uniform sphere of radius R and mass M rotates freely about a horizontal axis that is tangent to an equatorial plane of the sphere,as shown below.The moment of inertia of the sphere about this axis is
A)
.B)
.C)
.D)
.E)
. Unlock Deck
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61
Exhibit 10-2
The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track. Use this exhibit to answer the following question(s).
Refer to Exhibit 10-2.What is his average angular acceleration,in rad/s2,in the period from t = 6 min to t = 8 min?
A)0
B)
C)
D)
E)
The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track.
Use this exhibit to answer the following question(s).Refer to Exhibit 10-2.What is his average angular acceleration,in rad/s2,in the period from t = 6 min to t = 8 min?
A)0
B)
C)
D)
E)
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62
Exhibit 10-3
The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s. Use this exhibit to answer the following question(s).
Refer to Exhibit 10-3.The angular position,θ,at t = 0 s is 3.0 rad,clockwise.The angular position,θ,at t = 7 s is
A)27 rad,CW.
B)27 rad,CCW.
C)33 rad,CW.
D)33 rad,CCW.
E)36 rad,CCW.
The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s.
Use this exhibit to answer the following question(s).Refer to Exhibit 10-3.The angular position,θ,at t = 0 s is 3.0 rad,clockwise.The angular position,θ,at t = 7 s is
A)27 rad,CW.
B)27 rad,CCW.
C)33 rad,CW.
D)33 rad,CCW.
E)36 rad,CCW.
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63
Exhibit 10-3
The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s. Use this exhibit to answer the following question(s).
Refer to Exhibit 10-3.The change in angular position,Δθ,during the 7-second period is
A)21 rad,CW.
B)21 rad,CCW.
C)30 rad,CW.
D)30 rad,CCW.
E)39 rad,CCW.
The graph below shows a plot of angular velocity in rad/s versus time in s from t = 0 s to t = 7 s.
Use this exhibit to answer the following question(s).Refer to Exhibit 10-3.The change in angular position,Δθ,during the 7-second period is
A)21 rad,CW.
B)21 rad,CCW.
C)30 rad,CW.
D)30 rad,CCW.
E)39 rad,CCW.
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64
A solid sphere,a solid cylinder,and a hoop all have the same mass and radius.Each are sent down identical inclined planes starting from rest.Their kinetic energies at the bottom of the incline are Ksphere, Kcylinder,and Khoop.Which of the following is true?
A)Ksphere > Kcylinder
B)Khoop > Ksphere
C)Khoop > Kcylinder
D)Kcylinder > Khoop
E)No answer above is correct.
A)Ksphere > Kcylinder
B)Khoop > Ksphere
C)Khoop > Kcylinder
D)Kcylinder > Khoop
E)No answer above is correct.
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65
A solid sphere,a solid cylinder,a spherical shell,and a hoop all have the same mass and radius.Each are rolling on a horizontal surface with the same center of mass speed,and then they roll up identical inclines.Which one goes the greatest distance up its incline?
A)the hoop
B)the solid sphere
C)the spherical shell
D)the cylinder
E)They all go the same distance up their inclines.
A)the hoop
B)the solid sphere
C)the spherical shell
D)the cylinder
E)They all go the same distance up their inclines.
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66
When the center of a bicycle wheel has linear velocity
Relative to the ground,the velocity relative to the ground of point P' at the top of the wheel is
A)0.
B) .
C) .
D) .
E) .
Relative to the ground,the velocity relative to the ground of point P' at the top of the wheel is
A)0.
B)
.C)
.D)
.E)
. Unlock Deck
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67
A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod.Relative to the positive direction of the axis of rotation,the angular positions of the sphere are positive,its angular velocity is positive,and its angular acceleration is negative.The sphere is
A)rotating clockwise and slowing down.
B)rotating counterclockwise and slowing down.
C)rotating clockwise and speeding up.
D)rotating counterclockwise and speeding up.
E)first rotating clockwise and then counterclockwise.
A)rotating clockwise and slowing down.
B)rotating counterclockwise and slowing down.
C)rotating clockwise and speeding up.
D)rotating counterclockwise and speeding up.
E)first rotating clockwise and then counterclockwise.
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68
Exhibit 10-1
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s).
The angular speed of the hour hand of a clock,in rad/min,is
A) .
B) .
C) .
D)π.
E)120π.
The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.
Use this exhibit to answer the following question(s).The angular speed of the hour hand of a clock,in rad/min,is
A)
.B)
.C)
.D)π.
E)120π.
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69
The graph below shows a plot of angular acceleration in rad/s2 versus time from t = 0 s to t = 8 s.The change in angular velocity,Δω,during this 8-second period is
A) ,CW.
B) ,CCW.
C) ,CW.
D) ,CCW.
E) ,CW.
A)
,CW.B)
,CCW.C)
,CW.D)
,CCW.E)
,CW. Unlock Deck
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70
A rigid rod of length l rotates about an axis perpendicular to the rod,with one end of the rod fixed to the axis.Which of the following are equal at all points on the rod?
I.
The angular position
II.
The angular velocity
III.
The angular acceleration
IV.
The centripetal acceleration
V.
The tangential acceleration
A)I and II
B)I,II,and III
C)I,II,III and IV
D)I,II,III,IV and V
E)I,II and IV.
I.
The angular position
II.
The angular velocity
III.
The angular acceleration
IV.
The centripetal acceleration
V.
The tangential acceleration
A)I and II
B)I,II,and III
C)I,II,III and IV
D)I,II,III,IV and V
E)I,II and IV.
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71
A celestial object called a pulsar emits its light in short bursts that are synchronized with its rotation.A pulsar in the Crab Nebula is rotating at a rate of 30 revolutions/second.What is the maximum radius of the pulsar,if no part of its surface can move faster than the speed of light (3 × 108 m/s)?
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72
Which of the following diagrams shows the greatest magnitude net torque with a zero net force? All the rods,of length 2r,rotate about an axis that is perpendicular to the rod and fixed in the center of the rod.All the forces are of magnitude F or 2F and all distances from the axis are r or r/2.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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73
When a wheel is rolling without slipping,the magnitude of its velocity relative to the ground is greatest at
A)the point in contact with the ground.
B)the point at the center of the wheel.
C)the point at the top of the wheel opposite to the point in contact with the ground.
D)the point farthest forward from the center of mass of the wheel.
E)the point farthest behind the center of mass of the wheel.
A)the point in contact with the ground.
B)the point at the center of the wheel.
C)the point at the top of the wheel opposite to the point in contact with the ground.
D)the point farthest forward from the center of mass of the wheel.
E)the point farthest behind the center of mass of the wheel.
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74
The graph below shows a plot of angular acceleration in rad/s2 versus time from t = 0 s to t = 8 s.The angular velocity at t = 0 s is
,CCW.The angular velocity,ω,at t = 8 s is
A) ,CW.
B) ,CCW.
C) ,CW.
D) ,CCW.
E) ,CW.
,CCW.The angular velocity,ω,at t = 8 s is
A)
,CW.B)
,CCW.C)
,CW.D)
,CCW.E)
,CW. Unlock Deck
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75
The net work done in accelerating a propeller from rest to an angular velocity of 200 rad/s is 3 000 J.What is the moment of inertia of the propeller?
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76
Exhibit 10-2
The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track. Use this exhibit to answer the following question(s).
Refer to Exhibit 10-2.What is his average angular acceleration,in rad/s2,in the first 10 minutes?
A)0
B)
C)
D)
E)
The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track.
Use this exhibit to answer the following question(s).Refer to Exhibit 10-2.What is his average angular acceleration,in rad/s2,in the first 10 minutes?
A)0
B)
C)
D)
E)
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77
A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod.Relative to the positive direction of the axis of rotation,the angular positions of the sphere are negative,its angular velocity is negative,and its angular acceleration is negative.The sphere is
A)rotating clockwise and slowing down.
B)rotating counterclockwise and slowing down.
C)rotating clockwise and speeding up.
D)rotating counterclockwise and speeding up.
E)first rotating counterclockwise and then clockwise.
A)rotating clockwise and slowing down.
B)rotating counterclockwise and slowing down.
C)rotating clockwise and speeding up.
D)rotating counterclockwise and speeding up.
E)first rotating counterclockwise and then clockwise.
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78
A horizontal force of magnitude 6.5 N is exerted tangentially on a Frisbee of mass 32 grams and radius 14.3 cm.Assuming the Frisbee,a uniform disk,is originally at rest and the force is exerted for 0.08 s,determine the angular velocity of rotation about the central axis when the Frisbee is released.
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79
When the sum of the external forces and the sum of the external torques on a body are both zero,we can conclude that
A)the body is moving at constant velocity but is not rotating.
B)the body is rotating at constant angular velocity but has no linear velocity.
C)the body has neither linear nor angular velocity.
D)the body may have constant linear or angular velocity,but not both simultaneously.
E)the body may have constant linear or constant angular velocity,or both simultaneously.
A)the body is moving at constant velocity but is not rotating.
B)the body is rotating at constant angular velocity but has no linear velocity.
C)the body has neither linear nor angular velocity.
D)the body may have constant linear or angular velocity,but not both simultaneously.
E)the body may have constant linear or constant angular velocity,or both simultaneously.
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80
A small sphere attached to a light rigid rod rotates about an axis perpendicular to and fixed to the other end of the rod.Relative to the positive direction of the axis of rotation,the angular positions of the sphere are negative,its angular velocity is negative,and its angular acceleration is positive.The sphere is
A)rotating clockwise and slowing down.
B)rotating counterclockwise and slowing down.
C)rotating clockwise and speeding up.
D)rotating counterclockwise and speeding up.
E)first rotating counterclockwise and then clockwise.
A)rotating clockwise and slowing down.
B)rotating counterclockwise and slowing down.
C)rotating clockwise and speeding up.
D)rotating counterclockwise and speeding up.
E)first rotating counterclockwise and then clockwise.
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