Deck 9: Rotational Motion

Question 1

A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane,and they roll down without slipping.Which one 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.

Answer 1

D

Question 2

The figure shows scale drawings of four objects,each of the same mass and uniform thickness,with the mass distributed uniformly.Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P?

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

Answer 2

B

Question 3

Consider a solid uniform sphere of radius R and mass M rolling without slipping.Which form of its kinetic energy is larger,translational or rotational?

A)Translational kinetic energy is larger.
B)Rotational kinetic energy is larger.
C)Both are equal.
D)You need to know the speed of the sphere to tell.

Answer 3

A

Question 4

A spinning ice skater is able to control the rate at which she rotates by pulling in her arms.Which of the following statements are true about the skater during this process? (There could be more than one correct choice.)

A)Her angular momentum remains almost constant.
B)Her moment of inertia remains almost constant.
C)Her kinetic energy remains almost constant.
D)She is subject to a constant non-zero torque.

Question 5

Suppose a uniform solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest.The linear velocity of the sphere at the bottom of the incline depends on

A)the mass of the sphere.
B)the radius of the sphere.
C)both the mass and the radius of the sphere.
D)neither the mass nor the radius of the sphere.

Question 6

Two children,Ahmed and Jacques,ride on a merry-go-round.Ahmed is at a greater distance from the axis of rotation than Jacques.Which of the following are true statements? (There could be more than one correct choice.)

A)Jacques has a greater angular speed than Ahmed.
B)Jacques and Ahmed have the same angular speed.
C)Jacques has a smaller angular speed than Ahmed.
D)Ahmed has a greater tangential speed than Jacques.
E)Jacques and Ahmed have the same tangential speed.

Question 7

When is the angular momentum of a system constant?

A)Only when its total kinetic energy is constant.
B)Only when the linear momentum and the energy are constant.
C)Only when no net external torque is exerted on the system.
D)Only when the moment of inertia is constant.

Question 8

A car is traveling along a freeway at 65 mph.What is the linear speed,relative to the highway,of each of the following points on one of its tires?
(a)the highest point on the tire
(b)the lowest point on a tire
(c)the center of the tire

Question 9

A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane.If both are uniform,which one reaches the bottom of the incline first if there is no slipping?

A)The hoop
B)The disk
C)Both reach the bottom at the same time.

Question 10

Consider a uniform hoop of radius R and mass M rolling without slipping.Which is larger,its translational kinetic energy or its rotational kinetic energy?

A)Translational kinetic energy is larger.
B)Rotational kinetic energy is larger.
C)Both are equal.
D)You need to know the speed of the hoop to tell.

Question 11

A disk,a hoop,and a solid sphere are released at the same time at the top of an inclined plane.They are all uniform and roll without slipping.In what order do they reach the bottom?

A)disk, hoop, sphere
B)hoop, sphere, disk
C)sphere, disk, hoop
D)sphere, hoop, disk
E)hoop, disk, sphere

Question 12

Suppose a solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest.The angular velocity of the sphere at the bottom of the incline depends on

A)the mass of the sphere.
B)the radius of the sphere.
C)both the mass and the radius of the sphere.
D)neither the mass nor the radius of the sphere.

Question 13

A uniform ball is released from rest on a no-slip surface,as shown in the figure.After reaching its lowest point,the ball begins to rise again,this time on a frictionless surface.When the ball reaches its maximum height on the frictionless surface,it is

A)higher than when it was released.
B)lower than when it was released.
C)at the same height from which it was released.
D)It is impossible to tell without knowing the mass of the ball.
E)It is impossible to tell without knowing the radius of the ball.

Question 14

Two uniform solid balls,one of radius R and mass M,the other of radius 2R and mass 8M,roll down a high incline.They start together from rest at the top of the incline.Which one will reach the bottom of the incline first?

A)The small sphere arrives first.
B)Both reach the bottom at the same time.
C)The large sphere arrives first.

Question 15

A person sits on a freely spinning lab stool that has no friction in its axle.When this person extends her arms,

A)her moment of inertia decreases and her angular speed increases.
B)her moment of inertia decreases and her angular speed decreases.
C)her moment of inertia increases and her angular speed increases.
D)her moment of inertia increases and her angular speed decreases.
E)her moment of inertia increases and her angular speed remains the same.

Question 16

When a rigid object rotates about a fixed axis,what is true about all the points in the object? (There could be more than one correct choice.)

A)They all have the same angular speed.
B)They all have the same tangential speed.
C)They all have the same angular acceleration.
D)They all have the same tangential acceleration.
E)They all have the same radial acceleration.

Question 17

A solid sphere,solid cylinder,and a hollow pipe all have equal masses and radii.If the three of them are released simultaneously at the top of an inclined plane and do not slip,which one will reach the bottom first?

A)sphere
B)pipe
C)cylinder
D)The pipe and cylinder arrive together before the sphere.
E)They all reach the bottom at the same time.

Question 18

A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round.As he does this,it is true to say that

A)the moment of inertia of the system decreases and the angular speed increases.
B)the moment of inertia of the system decreases and the angular speed decreases.
C)the moment of inertia of the system decreases and the angular speed remains the same.
D)the moment of inertia of the system increases and the angular speed increases.
E)the moment of inertia of the system increases and the angular speed decreases.

Question 19

A solid sphere and a solid cylinder,both uniform and of the same mass and radius,roll without slipping at the same forward speed.It is correct to say that the total kinetic energy of the solid sphere is

A)more than the total kinetic energy of the cylinder.
B)less than the total kinetic energy of the cylinder.
C)equal to the total kinetic energy of the cylinder.

Question 20

The rotating systems shown in the figure differ only in that the two identical movable blocks are positioned a distance r from the axis of rotation (left),or a distance r/2 from the axis of rotation (right).If you release the hanging blocks simultaneously from rest,

A)the block at the left lands first.
B)the block at the right lands first.
C)both blocks land at the same time.

Question 21

An artificial satellite in a low orbit circles the earth every 98 minutes.What is its angular speed in rad/s?

Question 22

A child is riding a merry-go-round that is turning at 7.18 rpm.If the child is standing 4.65 m from the center of the merry-go-round,how fast is the child moving?

A)5.64 m/s
B)3.50 m/s
C)0.556 m/s
D)1.75 m/s
E)1.80 m/s

Question 23

A rolling wheel of diameter of 68 cm slows down uniformly from 8.4 m/s to rest over a distance of 115 m.What is the magnitude of its angular acceleration if there was no slipping?

A)1.8 rad/s²
B)0.90 rad/s²
C)5.7 rad/s²
D)11 rad/s²

Question 24

A wheel of diameter 0.70 m rolls on the floor without slipping.A point at the top of the wheel moves with a speed 2.0 m/s relative to the floor.
(a)At what speed is the central axis of the wheel moving relative to the floor?
(b)What is the angular speed of the wheel?

Question 25

At a certain instant,a compact disc is rotating at 210 rpm.What is its angular speed in rad/s?

A)11 rad/s
B)22 rad/s
C)45 rad/s
D)69 rad/s
E)660 rad/s

Question 26

A bowling ball of mass 7.5 kg and diameter 18 cm rolls without slipping down a 10-m bowling lane with a constant speed 4.3 m/s.
(a)Through what angle does the bowling ball turn as it travels the length of the lane?
(b)What is the angular speed of the bowling ball?
(c)Calculate the maximum radial acceleration that a point on the surface of the bowling ball could have.
(d)Calculate the tangential acceleration of a point on the surface of the bowling ball.

Question 27

Through how many degrees does a 33 rpm turntable rotate in

A)63°
B)35°
C)46°
D)74°

Question 28

The diameter of the Moon is 3.47 × 10⁶ m,and it subtends an angle of 0.00904 rad when viewed from the surface of Earth.How far is the Moon from Earth?

Question 29

A bicycle has wheels that are 60 cm in diameter.What is the angular speed of these wheels when it is moving at 4.0 m/s?

A)1.2 rad/s
B)4.8 rad/s
C)0.36 rad/s
D)13 rad/s
E)7.6 rad/s

Question 30

Express the angular speed of an old 33 1/3 rpm LP in rad/s.

Question 31

A cylinder of radius 8.0 cm rolls 20 cm in 5.0 s without slipping.Through how many degrees does the cylinder turn during this time?

Question 32

When Mary is 3.00 m from the center of a merry-go-round,her tangential speed is a constant 1.88 m/s.
(a)What is her angular speed in rad/s?
(b)What is the magnitude of her linear acceleration?

Question 33

A scooter has wheels with a diameter of 120 mm.What is the angular speed of the wheels when the scooter is moving forward at 6.00 m/s?

A)47.7 rpm
B)955 rpm
C)72.0 rpm
D)50.0 rpm
E)100 rpm

Question 34

A chicken is running in a circular path with an angular speed of 1.52 rad/s.How long does it take the chicken to complete one revolution?

A)4.13 s
B)2.07 s
C)118 s
D)4.77 s
E)8.26 s

Question 35

A bicycle wheel has an outside diameter of 66 cm.Through what distance does a point on the rim move as the wheel rotates through an angle of 70°?

Question 36

A string is wound tightly around a fixed pulley having a radius of 5.0 cm.As the string is pulled,the pulley rotates without any slipping of the string.What is the angular speed of the pulley when the string is moving at 5.0 m/s?

A)100 rad/s
B)50 rad/s
C)25 rad/s
D)20 rad/s
E)10 rad/s

Question 37

An electrical motor spins at a constant If the rotor radius is what is the linear 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 38

What is the angular speed,in rad/s,of a flywheel turning at 813.0 rpm?

A)85.14 rad/s
B)13.53 rad/s
C)63.84 rad/s
D)95.33 rad/s

Question 39

When a fan is turned off,its angular speed decreases from 10 rad/s to 6.3 rad/s in 5.0 s.What is the magnitude of the average angular acceleration of the fan?

A)0.86 rad/s²
B)0.74 rad/s²
C)0.37 rad/s²
D)11 rad/s²
E)1.2 rad/s²

Question 40

The sun subtends an angle of 0.00928 rad when viewed from the surface of the earth,and its distance from Earth is 1.5 × 10¹¹ m.What is the diameter of the sun?

Question 41

A machinist turns on the power on to a grinding wheel at time t = 0 s.The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of The wheel is run at that angular velocity for 30 s,and then power is shut off.The wheel slows down uniformly at until the wheel stops.What is the total number of revolutions made by the wheel in this situation?

A)510
B)280
C)320
D)470
E)750

Question 42

A wheel accelerates with a constant angular acceleration of 4.5 rad/s² from an initial angular speed of 1.0 rad/s.(a)Through what angle does the wheel turn in the first 2.0 s,and (b)what is its angular speed at that time?

Question 43

An old LP record that is originally rotating at 33.3 rad/s has a uniform angular acceleration of 2.15 rad/s².Through what angle has the record turned when its angular speed reaches 72.0 rad/s?

A)83.2 rad
B)316 rad
C)697 rad
D)66.8 rad
E)948 rad

Question 44

A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/min.When switched off,it makes 50 complete turns at a constant angular acceleration before coming to rest.
(a)What was the magnitude of the angular acceleration of the centrifuge as it slowed down?
(d)How long did it take for the centrifuge to come to rest after being turned off?

Question 45

In the figure,point P is on the rim of a wheel of radius 2.0 m.At time t = 0,the wheel is at rest,and P is on the x-axis.The wheel undergoes a uniform counterclockwise angular acceleration of 0.010 rad/s² about the center O.
(a)At time t = 0,what is the tangential acceleration of P?
(b)What is the linear speed of P when it reaches the y-axis?
(c)What is the magnitude of the net linear acceleration of P when it reaches the y-axis?
(d)How long after starting does it take for P to return to its original position on the x-axis?

Question 46

An old 78 rpm record rotates through an angle of 320° as it slows down uniformly from 78.0 rpm to 22.8 rpm.What is the magnitude of the angular acceleration of the record?

A)2.34 rad/s²
B)5.46 rad/s²
C)6.50 rad/s²
D)8.35 rad/s²
E)10.9 rad/s²

Question 47

A Ferris wheel rotating at 20 rad/s slows down with a constant angular acceleration of magnitude 5.0 rad/s².How many revolutions does it make while slowing down before coming to rest?

A)40
B)20
C)6.4
D)3.2

Question 48

A wheel starts from rest and has a uniform angular acceleration of 4.0 rad/s².After the wheel completes its first revolution,how long does it take for it to make its second complete revolution?

Question 49

A child is riding a merry-go-round that has an instantaneous angular speed of 1.25 rad/s and an angular acceleration of 0.745 rad/s².The child is standing 4.65 m from the center of the merry-go-round.What is the magnitude of the linear acceleration of the child?

A)8.05 m/s²
B)7.27 m/s²
C)2.58 m/s²
D)3.46 m/s²
E)4.10 m/s²

Question 50

A machinist turns on the power to a grinding wheel at time t = 0 s.The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of The wheel is run at that angular speed 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,what is the angular acceleration of the wheel between t = 0 and t = 10s?

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

Question 51

A triatomic molecule is oriented as follows along the x-axis: atom 1 of mass m is at the origin,atom 2 of mass 2m is at x = a,and,atom 3 of mass 3m is at x = 2a.What is the moment of inertia of this molecule about the y-axis?

A)2ma²
B)3ma²
C)12ma²
D)14ma²

Question 52

When an old LP turntable was revolving at 33 rpm,it was shut off and uniformly slowed down and stopped in 5.5 seconds.
(a)What was the magnitude of its angular acceleration (in rad/s²)as it slowed down?
(b)Through how many revolutions did it turn while stopping?

Question 53

A wheel accelerates from rest to at a uniform rate of 58 rad/s²_. Through what angle (in radians)did the wheel turn while accelerating?

A)30 rad
B)24 rad
C)60 rad
D)38 rad

Question 54

How long does it take for a rotating object to speed up from 15.0 rad/s to 33.3 rad/s if it has a uniform angular acceleration of 3.45 rad/s²?

A)4.35 s
B)5.30 s
C)9.57 s
D)10.6 s
E)63.1 s

Question 55

A majorette fastens two batons together at their centers to form an X shape.Each baton consists of an extremely light 1.2-m bar with small 0.25-kg balls at each end.What is the moment of inertia of this baton about an axis through the center of the X?

Question 56

A turntable 45 cm in diameter starts from rest and makes its first complete revolution in 3.4 s with constant angular acceleration.If it maintains the same acceleration,how long will it take the turntable to make its second complete revolution?

Question 57

A wheel rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s.What is the magnitude of the angular acceleration of the wheel?

A)0.616 rad/s²
B)5.45 rad/s²
C)111 rad/s²
D)22.5 rad/s²
E)10.9 rad/s²

Question 58

A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 rad/s².Through what angle does the pulley turn in 5.26 s?

A)113 rad
B)22.6 rad
C)42.6 rad
D)19.3 rad
E)160 rad

Question 59

A machinist turns on the power on to a grinding wheel at time t = 0 s.The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of The wheel is run at that angular velocity for 40 s and then power is shut off.The wheel slows down uniformly at until the wheel stops.For how long a time after the power is shut off does it take the wheel to stop?

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

Question 60

A bicycle wheel has an initial angular speed of 7.2 rad/s.After turning through of a revolution,the angular speed is reduced to 2.2 rad/s.If the angular acceleration of the wheel was constant during the motion,how long will it take the wheel to make the revolution?

Question 61

A string is wrapped tightly around a fixed pulley that has a moment of inertia of 0.0352 kg ∙ m² and a radius of 12.5 cm.An object of mass of 423 g is attached to the free end of the string.With the string vertical and taut,the object is gently released so it can descend doe to the gravitational force exerted on it by Earth.As the object descends,the string unwinds and causes the pulley to rotate,but does not slip on the pulley.What is the speed of the object after it has fallen through 1.25 m?

A)2.00 m/s
B)2.28 m/s
C)1.97 m/s
D)3.94 m/s
E)4.95 m/s

Question 62

A solid uniform sphere of mass 120 kg and radius 1.7 m starts from rest and rolls without slipping down an inclined plane of vertical height 5.3 m.What is the angular speed of the sphere at the bottom of the inclined plane?

A)5.1 rad/s
B)8.7 rad/s
C)9.7 rad/s
D)6.1 rad/s

Question 63

The L-shaped object shown in the figure consists of three small mass spheres connected by extremely light rods.Assume that the masses shown are accurate to three significant figures.What is the moment of inertia of this object (a)about the x-axis,and (b)about the y-axis?

Question 64

In the figure,a weightlifter's barbell consists of two identical small but dense spherical objects,each of mass 50 kg.These objects are connected by a thin 0.96-m rod with a mass of 24 kg.Find the moment of inertia of the barbell through the axis perpendicular to the rod at its center,assuming the two objects are small enough to be treated as point like objects.

Question 65

The L-shaped object shown in the figure consists of three small mass objects connected by extremely light rods.Assume that the masses shown are accurate to three significant figures.How much work must be done to accelerate the object from rest to an angular speed of 3.25 rad/s (a)about the x-axis,(b)about the y-axis?

Question 66

The L-shaped object shown in the figure consists of three small mass spheres connected by thin uniform rods,each rod of mass 3.00 kg.Assume that the masses shown are accurate to three significant figures.What is the moment of inertia of this object (a)about the x-axis,and (b)about the y-axis?

Question 67

A potter's wheel has the shape of a solid uniform disk of mass and radius 0.65 m.It spins about an axis perpendicular to the disk at its center.A small 2.1 kg lump of very dense clay is dropped onto the wheel at a distance 0.41 m from the axis.What is the moment of inertia of the system about the axis of spin?

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

Question 68

A solid uniform ball with a mass of 125 g is rolling without slipping along the horizontal surface of a table with a speed of 4.5 m/s when it rolls off the edge and falls towards the floor,1.1 m below.What is the rotational kinetic energy of the ball just before it hits the floor?

A)0.51 J
B)0.73 J
C)1.1 J
D)2.6 J
E)This question cannot be answered without knowing the radius of the ball.

Question 69

While spinning down from 500 rpm to rest,a flywheel does of work.This flywheel is in the shape of a solid uniform disk of radius 1.2 m.What is the mass of this flywheel?

A)4.0 kg
B)3.4 kg
C)4.6 kg
D)5.2 kg

Question 70

Two uniform solid spheres have the same mass,but one has twice the radius of the other.The ratio of the larger sphere's moment of inertia about a central axis to that of the smaller sphere is

A)4/5.
B)8/5.
C)1/2.
D)2.
E)4.

Question 71

A small ball is tied to one end of a light 2.5-m wire,and the other end of the wire is hooked to the ceiling.A person pulls the ball to the side until the wire makes an angle of 35° with the plane of the ceiling and then gently releases it.What is the angular speed of the ball,in rad/s,as it swings through its lowest point?

Question 72

A string is wrapped tightly around a fixed frictionless pulley that has a moment of inertia of 0.0352 kg ∙ m² and a radius of 12.5 cm.The string is pulled away from the pulley exerting a constant force of 5.00 N on the pullley causing the pulley to rotate.What is the speed of the string after it has unwound 1.25 m if the string does not slip on the pulley?

A)2.09 m/s
B)2.36 m/s
C)1.18m/s
D)3.18 m/s
E)4.95 m/s

Question 73

A futuristic design for a car is to have a large flywheel within the car to store kinetic energy.The flywheel is a solid uniform disk of mass 370 kg with a radius of 0.50 m,and it can rotate up to Assuming all of this stored kinetic energy could be transferred to the car to change its linear speed of,find the maximum attainable speed of the car.

Question 74

A solid uniform disk of diameter 3.20 m and mass 42 kg rolls without slipping to the bottom of a hill,starting from rest.If the angular speed of the disk is 4.27 rad/s at the bottom,how high did it start on the hill?

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

Question 75

What is the kinetic energy of a 120-cm thin uniform rod with a mass of 450 g that is rotating about its center at 3.60 rad/s?

A)0.350 J
B)4.20 J
C)0.700 J
D)0.960 J
E)2.10 J

Question 76

The L-shaped object shown in the figure consists of three small mass objects connected by thin uniform rods,each rod of mass 3.00 kg.Assume that the masses shown are accurate to three significant figures.How much work must be done to accelerate the object from rest to an angular speed of 3.25 rad/s about the y-axis?

Question 77

To drive a typical car at 40 mph on a level road for one hour requires about 3.2 × 10⁷ J of energy.Suppose we tried to store this much energy in a spinning,solid,uniform,cylindrical flywheel.A large flywheel cannot be spun too fast or it will fracture.If we used a flywheel of diameter 1.2 m and mass 400 kg,what angular speed would be required to store 3.2 × 10⁷ J?

A)1800 rad/s
B)3600 rad/s
C)940 rad/s
D)530 rad/s
E)5500 rad/s

Question 78

A uniform solid cylinder with a radius of 10 cm and a mass of 3.0 kg is rotating about its center with an angular speed of 33.4 rpm.What is its kinetic energy?

A)0.18 J
B)0.092 J
C)0.96 J
D)1.1 J
E)17 J

Question 79

As shown in the figure,two blocks are connected by a light string that passes over a frictionless pulley having a moment of inertia of 0.0040 kg ∙ m² and diameter 10 cm.The coefficient of kinetic friction between the table top and the upper block is 0.30.The blocks are released from rest,and the string does not slip on the pulley.How fast is the upper block moving when the lower one has fallen 0.60 m?

A)1.2 m/s
B)5.4 m/s
C)3.2 m/s
D)2.0 m/s
E)1.4 m/s

Question 80

A wheel having a moment of inertia of 5.00 kg ∙ m² starts from rest and accelerates under a constant torque of 3.00 N ∙ m for 8.00 s.What is the wheel's rotational kinetic energy at the end of 8.00 s?

A)57.6 J
B)64.0 J
C)78.8 J
D)122 J