Deck 10: Rotational Motion

Question 1

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)16 $\pi$
C)32 $\pi$
D)40 $\pi$
E)64 $\pi$

Answer 1

40 $\pi$

Question 2

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

Answer 2

24 rev

Question 3

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

Answer 3

14 rad/s²

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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) $\pi$
C)4 $\pi$
D)8 $\pi$
E)16 $\pi$

Question 9

A wheel rotating about a fixed axis has an angular position given by $\theta$ = 3.0 -2.0t³,where $\theta$ 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

Question 10

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

Question 11

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

Question 12

The angular speed of the hour hand of a clock,in rad/s,is

A) $\frac { 1 } { 7200 } \pi$ .
B) $\frac { 1 } { 1800 } \pi$ .
C) $\frac { 1 } { 30 } \pi$ .
D)1 800 $\pi$ .
E)7 200 $\pi$ .

Question 13

The angular speed of the minute hand of a clock,in rad/s,is

A) $\frac { 1 } { 1800 } \pi$ .
B) $\frac { 1 } { 60 } \pi$ .
C) $\frac { 1 } { 30 } \pi$ .
D) $\pi$ .
E)120 $\pi$ .

Question 14

The angular speed of the hour hand of a clock,in rad/min,is

A) $\frac { 1 } { 1800 } \pi$ .
B) $\frac { 1 } { 60 } \pi$ .
C) $\frac { 1 } { 30 } \pi$ .
D) $\pi$ .
E)120 $\pi$ .

Question 15

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

Question 16

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)

Question 17

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) $- \frac { \pi } { 150 }$
C) $- \frac { \pi } { 75 }$
D) $+ \frac { \pi } { 75 }$
E) $+ \frac { \pi } { 150 }$

Question 18

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)2 $\pi$
C)4 $\pi$
D)16 $\pi$
E)32 $\pi$

Question 19

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

Question 20

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

Question 21

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 $\degree$ 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

Question 22

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

Question 23

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, $\Delta$$\omega$ ,during this 8-second period is

A) $18 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CW.
B) $18 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CCW.
C) $23 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CW.
D) $23 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CCW.
E) $31 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CW.

Question 24

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) $- \frac { \pi } { 90 }$
C) $- \frac { \pi } { 30 }$
D) $+ \frac { \pi } { 30 }$
E) $+ \frac { \pi } { 90 }$

Question 25

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

Question 26

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

Question 27

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)0.24 m/s²
B)0.50 m/s²
C)0.14 m/s²
D)0.34 m/s²
E)0.20 m/s²

Question 28

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.

Question 29

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

Question 30

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.

Question 31

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 $$\omega _ { 0 } = 5 \frac { \mathrm { rad } } { \mathrm { s } }$$ ,CCW.The angular velocity, $\omega$ ,at t = 8 s is

A) $18 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CW.
B) $18 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CCW.
C) $23 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CW.
D) $23 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CCW.
E) $43 \frac { \mathrm { rad } } { \mathrm { s } }$ ,CW.

Question 32

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.

Question 33

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

Question 34

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

Question 35

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.

Question 36

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

Question 37

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

Question 38

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, $\theta$ ,at t = 0 s is 3.0 rad,clockwise.The angular position, $\theta$ ,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 39

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

Question 40

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, $\Delta$$\theta$ ,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.

Question 41

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)

Question 42

Two vectors lying in the xy plane are given by the equations $\overrightarrow { \mathbf { A } } = 5 \hat { \mathbf { i } } + 2 \hat { \mathbf { j } }$ and $\overrightarrow { \mathbf { B } } = 2 \hat { \mathbf { i } } - 3 \hat { \mathbf { j } }$ .The value of $\overrightarrow { \mathbf { A } } \times \overrightarrow { \mathbf { B } }$ is

A)19
B)-11 11eff292_fd3d_8945_958a_0f5e6e05e897_TB5764_00
C)-19 11eff292_fd3d_8945_958a_0f5e6e05e897_TB5764_00
D)11 11eff292_fd3d_8945_958a_0f5e6e05e897_TB5764_00
E)10

Question 43

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 $\degree$ below the horizontal?

A)15 rad/s²
B)12 rad/s²
C)18 rad/s²
D)29 rad/s²
E)23 rad/s²

Question 44

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) $\frac { 2 } { 5 } M R ^ { 2 }$ .
B) $\frac { 2 } { 3 } M R ^ { 2 }$ .
C) $\frac { 5 } { 7 } M R ^ { 2 }$ .
D) $\frac { 7 } { 5 } M R ^ { 2 }$ .
E) $\frac { 3 } { 2 } M R ^ { 2 }$ .

Question 45

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

Question 46

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.

Question 47

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

Question 48

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

Question 49

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

Question 50

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

Question 51

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

Question 52

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 kgF.m²
E)0.032 kg.m²

Question 53

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

Question 54

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

Question 55

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

Question 56

Two vectors lying in the xz plane are given by the equations $\overrightarrow { \mathbf { A } } = 2 \tilde { \mathbf { i } } + 3 \tilde { \mathbf { k } }$ and $\overrightarrow { \mathbf { B } } = - \tilde { \mathbf { i } } + 2 \tilde { \mathbf { k } }$ .The value of $$\overrightarrow { \mathbf { A } } \times \overrightarrow { \mathbf { B } }$$ is

A)
B) -11eff293_251a_c457_958a_a94006dbb7f5_TB5764_00
C)7 11eff293_251a_c457_958a_a94006dbb7f5_TB5764_00
D)-711eff293_251a_c457_958a_a94006dbb7f5_TB5764_00
E)

Question 57

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) $\frac { 1 } { 2 } M R ^ { 2 }$ .
B) $\frac { 2 } { 3 } M R ^ { 2 }$ .
C)MR².
D) $\frac { 3 } { 2 } M R ^ { 2 }$ .
E) $\frac { 7 } { 5 } M R ^ { 2 }$ .

Question 58

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

Question 59

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

Question 60

A particle located at the position vector $\hat { \mathbf { r } } = ( \tilde { \mathbf { i } } + \hat { \mathbf { j } } )$ m has a force $\overrightarrow { \mathbf { F } } = ( 2 \hat { \mathbf { i } } + 3 \tilde { \mathbf { j } } )$ N acting on it.The torque about the origin is

A)(1 )N.m
B)(5 11eff295_64b5_f60b_958a_2ba2e960c5d1_TB5764_00 )N.m
C)(-1 11eff295_64b5_f60b_958a_2ba2e960c5d1_TB5764_00 )N.m
D)(-5 11eff295_64b5_f60b_958a_2ba2e960c5d1_TB5764_00 )N.m
E)(2 $\hat { \mathbf { i } }$ + 3 $\hat { \mathbf {j} }$ )N.m

Question 61

Two blocks,m₁ = 1.0 kg and m₂ = 2.0 kg,are connected by a light string as shown in the figure.If the radius of the pulley is 1.0 m and its moment of inertia is 5.0 kg.m²,the acceleration of the system is

A)(1/6)g
B)(3/8)g
C)(1/8)g
D)(1/2)g
E)(5/8)g

Question 62

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

Question 63

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

Question 64

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 $\degree$ 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

Question 65

A massless rope is wrapped around a uniform cylinder that has radius R and mass M,as shown in the figure.Initially,the unwrapped portion of the rope is vertical and the cylinder is horizontal.The linear acceleration of the cylinder is

A)(2/3)g
B)(1/2)g
C)(1/3)g
D)(1/6)g
E)(5/6)g

Question 66

Five identical cylinders are each acted on by forces of equal magnitude.Which force exerts the biggest torque about the central axes of the cylinders?

A)
B)
C)
D)
E)

Question 67

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 $\degree$ 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

Question 68

Two objects of mass m₁ = 2m and m₂ = m move around a rotation axis A in parallel circles of radii r₁ = r and r₂ = 2r with equal tangential speeds.As they rotate,forces of equal magnitude are applied opposite to their velocities to stop them.Which statement is correct?

A)m₂ will stop first because it has the larger initial angular velocity.
B)m₁ will stop first because it has the smaller radius.
C)m₂ will stop first because the torque on it is greater.
D)m₁ will stop first because it has the smaller moment of inertia.
E)Both objects will stop at the same time because the angular accelerations are equal.

Question 69

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

Question 70

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; $\omega$ = 0.
B)v = 0; $\omega$ = 4.
C)v = 0; $\omega$ = 8.
D)v = 8; $\omega$ = 8.
E)v = 16; $\omega$ = 8.

Question 71

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 $\degree$ 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

Question 72

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

Question 73

A force $\overrightarrow { \mathrm { F } }$ is applied to a cylindrical roll of paper of radius R and mass M by pulling on the paper as shown.The acceleration of the center of mass of the roll of paper (when it rolls without slipping)is

A) $\frac { 1 } { 2 } \frac { F } { M }$ .
B) $\frac { F } { M }$ .
C) $\frac { 3 } { 2 } \frac { F } { M }$ .
D) $\frac { 4 } { 3 } \frac { F } { M }$ .
E) $\frac { 2 F } { M }$ .

Question 74

The diagram below shows five 20-kg rods of the same 2.0-m length free to rotate about axes through the rods,as indicated.Which rod experiences the greatest magnitude gravitational torque?

A)
B)
C)
D)
E)

Question 75

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, $\theta$ = 40 $\degree$ )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

Question 76

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 $\degree$ 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

Question 77

A torque can be exerted on a body with a fixed axis of rotation

A)only by a centripetal force.
B)only by a force directed radially outwards.
C)only by a tangential force.
D)only by a force with a component directed radially outwards.
E)by any force not pointing directly toward or away from the axis of rotation.

Question 78

A car of mass 1 000 kg moves with a speed of 50 m/s on a circular track of radius 100 m.What is the magnitude of its angular momentum (in kg.m²/s)relative to the center of the race track?

A)5.0 *10²
B)5.0 * 10⁶
C)2.5 * 10⁴
D)2.5 * 10⁶
E)5.0 *10³

Question 79

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

Question 80

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 $\degree$ 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