Deck 7: Rotational Motion

Question 1

A bicycle heading west at 2.0 m/s turns 90.0° to the left in 10.0 s.The final velocity of the bicycle after the turn is 4.2 m/s to the south.Find the direction of the wheel's average angular acceleration.Express your answer as an angle relative to east.

A)25° south of east
B)25° north of east
C)65° north of east
D)65° south of east

Answer 1

25° south of east

Question 2

A force of 17 N is applied to the end of a 0.63 m long torque wrench at an angle 45° from a line joining the pivot point to the handle.What is the magnitude of the torque generated about the pivot point?

A)7.6 N∙m
B)10.7 N∙m
C)12.0 N∙m
D)9.7 N∙m

Answer 2

7.6 N∙m

Question 3

A 95 N force exerted at the end of a 0.50 m long torque wrench gives rise to a torque of 15 N · m.What is the angle (assumed to be less than 90°)between the wrench handle and the direction of the applied force?

A)18°
B)14°
C)22°
D)25°

Answer 3

18°

Question 4

A 0.18 m radius pulley is free to rotate about a horizontal axis.A 4.2 kg mass and a 8.0 kg mass are attached by a massless string,which is hung over the pulley.If the string does not slip,calculate the magnitude of the net torque on the pulley about its rotational axis.

A)6.7 N ∙ m
B)5.5 N ∙ m
C)7.6 N ∙ m
D)9.5 N ∙ m

Question 5

A solid,uniform sphere of mass 2.0 kg and radius 1.7 m rolls without slipping down an inclined plane of height 7.0 m.What is the angular velocity of the sphere at the bottom of the inclined plane?

A)5.8 rad/s
B)9.9 rad/s
C)11.0 rad/s
D)7.0 rad/s

Question 6

A potter's wheel (a solid,uniform disk)of mass 7.0 kg and radius 0.65 m spins about its central axis.A 2.1 kg lump of clay is dropped onto the wheel at a distance 0.41 m from the axis.Calculate the rotational inertia of the system.

A)1.8 kg ∙ m²
B)1.5 kg ∙ m²
C)0.40 kg ∙ m²
D)2.5 kg ∙ m²

Question 7

A particular motor can provide a maximum of 110.0 N · m of torque.Assuming that all of this torque is used to accelerate a solid,uniform flywheel of mass 10.0 kg and radius 3.00 m,how long will it take for the flywheel to accelerate from rest to 6.04 rad/s?

A)2.47 s
B)2.10 s
C)2.99 s
D)3.24 s

Question 8

A machinist turns the power on to a grinding wheel,at rest,at time t = 0 s.The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 29 rad/s.The wheel is run at that angular velocity for 27 s and then power is shut off.The wheel slows down uniformly at 2.7 rad/s² until the wheel stops.In this situation,the average angular velocity in the time interval from t = 0 s to t = 25 s is closest to:

A)17 rad/s
B)15 rad/s
C)13 rad/s
D)11 rad/s
E)8.7 rad/s

Question 9

Through what angle in degrees does a 33 rpm record turn in 0.32 s?

A)63°
B)35°
C)46°
D)74°

Question 10

A solid disk of radius 1.60 m and mass 2.30 kg rolls without slipping to the bottom of an inclined plane.If the angular velocity of the disk is 4.27 rad/s at the bottom,what is the height of the inclined plane?

A)3.57 m
B)2.68 m
C)3.14 m
D)4.28 m

Question 11

A machinist turns the power on to a grinding wheel,at rest,at time t = 0 s.The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 96 rad/s.The wheel is run at that angular velocity for 40 s and then power is shut off.The wheel slows down uniformly at 1.5 rad/s² until the wheel stops.In this situation,the time interval of deceleration is closest to:

A)64 s
B)62 s
C)66 s
D)68 s
E)70 s

Question 12

At time t = 0 s,a wheel has an angular displacement of zero radians and an angular velocity of +28 rad/s.The wheel has a constant acceleration of -0.51 rad/s².In this situation,the time t,at which the wheel comes to a mandatory halt,is closest to:

A)130 s
B)120 s
C)96 s
D)78 s
E)55 s

Question 13

A child is sitting on the outer edge of a merry-go-round that is 18 m in diameter.If the merry-go-round makes 4.9 rev/min,what is the velocity of the child in m/s?

A)4.6 m/s
B)9.2 m/s
C)0.7 m/s
D)3.2 m/s

Question 14

The table shows the masses and the coordinates x and y of a set of three point masses in the x-y plane.The masses are interconnected by light struts,forming a rigid body.The moment of inertia of the rigid body,through the center of mass and perpendicular to the x-y plane,is closest to:

A)3000 kg ∙ m²
B)3200 kg ∙ m²
C)3400 kg ∙ m²
D)3600 kg ∙ m²
E)3800 kg ∙ m²

Question 15

A solid disk of radius 1.60 m and mass 2.30 kg rolls without slipping to the bottom of an inclined plane.If the angular velocity of the disk is 5.35 rad/s at the bottom,what is the height of the inclined plane?

A)5.61 m
B)4.21 m
C)4.94 m
D)6.73 m

Question 16

An electrical motor spins at a constant 2695.0 rpm.If the armature radius is 7.165 cm,what is the acceleration of the edge of the rotor?

A)5707 m/s²
B)281.6 m/s²
C)572,400 m/s²
D)28.20 m/s²

Question 17

A wheel accelerates from rest to 59 rad/s at a rate of 74 rad/s².Through what angle (in radians)did the wheel turn while accelerating?

A)24 rad
B)19 rad
C)48 rad
D)30 rad

Question 18

A machinist turns the power on to a grinding wheel,at rest,at time t = 0 s.The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 38 rad/s.The wheel is run at that angular velocity for 30 s and then power is shut off.The wheel slows down uniformly at 2.1 rad/s² until the wheel stops.In this situation,the angular acceleration of the wheel between t = 0 s and t = 10 s is closest to:

A)3.8 rad/s²
B)4.6 rad/s²
C)5.3 rad/s²
D)6.1 rad/s²
E)6.8 rad/s²

Question 19

A torque of 12 N ∙ m is applied to a solid,uniform disk of radius 0.50 m.If the disk accelerates at 5.7 rad/s²,what is the mass of the disk?

A)17 kg
B)13 kg
C)8.5 kg
D)4.3 kg

Question 20

A force in the +y direction applied at the point x = 2.3 m,y = 1.4 m gives rise to a torque of 71 N · m about the origin.Find the magnitude of the force.

A)31 N
B)51 N
C)71 N
D)87 N

Question 21

If a spinning object has a negative angular acceleration,it must be slowing down.

Question 22

A cylinder and a sphere,both solid and uniform and having the same mass and diameter,roll without slipping down the same ramp starting from rest.Both of them will reach the ground at the same time.

Question 23

A tire is rolling along a road,without slipping,with a velocity v.A piece of tape is attached to the tire.When the tape is opposite the road (at the top of the tire),it's velocity with respect to the road is

A)2 v.
B)v.
C)1.5 v.
D)The velocity depends on the radius of the tire.

Question 24

At time t = 0 s,a wheel has an angular displacement of zero radians and an angular velocity of +14 rad/s.The wheel has a constant acceleration of -0.41 rad/s².In this situation,the time at which the angular displacement is + 88 rad and decreasing is closest to:

A)61 s
B)34 s
C)7 s
D)6 s
E)74 s

Question 25

In the figure,a mass of 35.30 kg is attached to a light string that is wrapped around a cylindrical spool of radius 10 cm and moment of inertia 4.00 kg · m2.The spool is suspended from the ceiling,and the mass is then released from rest a distance 3.50 m above the floor.How long does it take to reach the floor?

A)2.97 s
B)2.85 s
C)0.892 s
D)4.18 s
E)5.89 s

Question 26

A light triangular plate OAB is in a horizontal plane.Three forces,F₁ = 2 N,F₂ = 4 N,and F₃ = 7 N,act on the plate,which is pivoted about a vertical axis through point O.In the figure,consider the counterclockwise sense as positive.The sum of the torques about the vertical axis through point O,acting on the plate due to forces F₁,F₂,and F₃,is closest to:

A)2.2 N ∙ m
B)2.6 N ∙ m
C)-2.2 N ∙ m
D)-2.6 N ∙ m
E)zero

Question 27

A rectangular sign h = 20.0 cm high and w = 11.0 cm wide loses three of its four support bolts and rotates into the position as shown,with P₁ directly over P₃.It is supported by P₂,which is so tight it holds the sign from further rotation.Find the gravitational torque about P₂,if the mass of the sign is 5.0 kg.

A)4.7 Nm
B)2.6 Nm
C)0.27 Nm
D)0.48 Nm

Question 28

If two objects have the same moment of inertia,they must have the same mass.

Question 29

There must be equal amounts of mass on either side of the center of mass.

Question 30

A disk and a sphere are released simultaneously at the top of an inclined plane.They roll down without slipping.Which will reach the bottom first?

A)the one of smallest diameter
B)the one of greatest mass
C)the disk
D)the sphere
E)They will reach the bottom at the same time.

Question 31

In the figure are scale drawings of four objects,each of the same mass and uniform thickness.Which has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing? In each case the axis passes through point P.

A)A
B)B
C)C
D)D
E)The moment of inertia is the same for all of these objects.

Question 32

A tall tree and a short tree (both having the same width and mass density)are cut at the base at the same time,and begin tipping over.Which tree hits the ground first?

A)the small tree
B)the tall tree
C)They hit at the same time.

Question 33

A small mass is placed on a record turntable that is rotating at 45 rpm.The linear acceleration of the mass is

A)directed perpendicular to the line joining the mass and the center of rotation.
B)independent (in magnitude)of the position of the mass on the turntable.
C)greater the closer the mass is to the center.
D)greater the farther the mass is from the center.
E)zero.

Question 34

A force of 16.88 N is applied tangentially to a wheel of radius 0.340 m and gives rise to an angular acceleration of 1.20 rad/s².Calculate the rotational inertia of the wheel.

A)4.78 kg ∙ m²
B)3.59 kg ∙ m²
C)5.98 kg ∙ m²
D)7.17 kg ∙ m²

Question 35

If you deform an object,you do not change its mass but you may change its moment of inertia and the location of its center of mass.

Question 36

A particular motor can provide a maximum of 110.0 N · m of torque.Assuming that all of this torque is used to accelerate a solid,uniform flywheel of mass 10.0 kg and radius 3.00 m,how long will it take for the flywheel to accelerate from rest to 8.13 rad/s?

A)3.33 s
B)2.83 s
C)4.03 s
D)4.36 s

Question 37

In the figure,a given force F is applied to a rod in several different ways.In which case is the torque due to F about the pivot P greatest?

A)1
B)2
C)3
D)4
E)5