Deck 10: Rotational Kinematics and Energy

Question 1

A car is traveling along a highway at 65 mph. What is the linear speed of the top of the tires?
What is the linear speed at the bottom of the tires?

Answer 1

130 mph; 0 mph

Question 2

When a rigid body rotates about a fixed axis all the points in the body have the same angular displacement.

Answer 2

True

Question 3

When a rigid body rotates about a fixed axis all the points in the body have the same centripetal acceleration.

Answer 3

False

Question 4

When a rigid body rotates about a fixed axis all the points in the body have the same tangential speed.

Question 5

When a rigid body rotates about a fixed axis all the points in the body have the same angular acceleration.

Question 6

Rolling without slipping depends on static friction between the rolling object and the ground.

Question 7

A car is traveling along a highway at 65 mph. Which point in the tires is moving forward at 65 mph?

Question 8

A hollow cylinder and a solid cylinder are constructed so they have the same mass and radius. Which cylinder has the larger moment of inertia?

Question 9

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger tangential acceleration?

A) Child A
B) Child B
C) They have the same zero centripetal acceleration.
D) They have the same non-zero centripetal acceleration.
E) There is not enough information given to answer the question.

Question 10

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger linear displacement?

A) Child A
B) Child B
C) They have the same zero linear displacement.
D) They have the same non-zero linear displacement.
E) There is not enough information given to answer the question.

Question 11

The preferred positive direction for angular displacement is the clockwise direction.

Question 12

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger centripetal acceleration?

A) Child A
B) Child B
C) They have the same zero centripetal acceleration.
D) They have the same non-zero centripetal acceleration.
E) There is not enough information given to answer the question.

Question 13

A car is moving in a circular path. At a certain instant, it has zero tangential acceleration and a non-zero centripetal acceleration. What is the car doing at that instant?

Question 14

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger angular speed?

A) Child A
B) Child B
C) They have the same zero angular speed.
D) They have the same non-zero angular speed.
E) There is not enough information given to answer the question.

Question 15

Mass can be considered concentrated at the center of mass for rotational motion.

Question 16

When a rigid body rotates about a fixed axis all the points in the body have the same linear displacement.

Question 17

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger angular displacement?

A) Child A
B) Child B
C) They have the same zero angular displacement.
D) They have the same non-zero angular displacement.
E) There is not enough information given to answer the question.

Question 18

When a rigid body rotates about a fixed axis all the points in the body have the same angular speed.

Question 19

Two children are riding on a merry-go-round. Child A is at a greater distance from the axis of rotation than child B. Which child has the larger tangential speed?

A) Child A
B) Child B
C) They have the same zero tangential speed.
D) They have the same non-zero tangential speed.
E) There is not enough information given to answer the question.

Question 20

When a rigid body rotates about a fixed axis all the points in the body have the same tangential acceleration.

Question 21

Rolling without slipping depends on

A) kinetic friction between the rolling object and the ground.
B) static friction between the rolling object and the ground.
C) normal force between the rolling object and the ground.
D) tension between the rolling object and the ground.
E) the force of gravity between the rolling object and the earth.

Question 22

Two children ride on a merry-go-round, George is at a greater distance from the axis of rotation than Jacques. It is a true statement that

A) Jacques has a greater angular velocity than George.
B) Jacques and George have the same angular velocity.
C) Jacques has a smaller angular velocity than George.
D) both have zero angular velocities.
E) Cannot tell which one has the greater angular velocity without knowing their masses.

Question 23

A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane. Which object reaches the bottom of the incline first?

A) The hoop
B) The disk
C) Both reach the bottom at the same time.
D) It depends on the angle of inclination.
E) It depends on the length of the inclined surface.

Question 24

FIGURE 10-1
A ball is released from rest on a no-slip surface, as shown. After reaching its lowest point, the ball begins to rise again, this time on a frictionless surface as shown in Figure 10-1. When the ball reaches its maximum height on the frictionless surface, it is

A) at a greater height as when it was released.
B) at a lesser height as when it was released.
C) at the same height as when it was released.
D) impossible to tell without knowing the mass of the ball.
E) impossible to tell without knowing the radius of the ball.

Question 25

Suppose a solid 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 26

A boy and a girl are riding a merry-go-round which is turning at a constant rate. The boy is near the outer edge, while the girl is closer to the center. Who has the greater tangential acceleration?

A) the boy
B) the girl
C) Both have the same non-zero tangential acceleration.
D) Both have zero tangential acceleration.
E) There is not enough information given to answer the question.

Question 27

Consider a hoop of radius R and mass M rolling without slipping. Which form of 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 hoop to tell.
E) You need to know the acceleration of the hoop to tell.

Question 28

A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii. If the three are released simultaneously at the top of an inclined plane, which will reach the bottom first?

A) sphere
B) pipe
C) cylinder
D) they all reach bottom in the same time
E) It depends on the angle of inclination.

Question 29

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 to that of the smaller sphere is

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

Question 30

A solid cylinder is rolling without slipping. What fraction of its kinetic energy is rotational?

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

Question 31

A boy and a girl are riding on a merry-go-round that is turning. The boy is twice as far as the girl from the merry-go-round's center. If the boy and girl are of equal mass, which statement is true about the boy's moment of inertia with respect to the axis of rotation?

A) His moment of inertia is 4 times the girl's.
B) His moment of inertia is twice the girl's.
C) The moment of inertia is the same for both.
D) The boy has a greater moment of inertia, but it is impossible to say exactly how much more.
E) The boy has a smaller moment of inertia, but it is impossible to say exactly how much smaller.

Question 32

Two children ride on a merry-go-round, George is at a greater distance from the axis of rotation than Jacques. It is a true statement that

A) Jacques has a greater tangential speed than George.
B) Jacques and George have the same tangential speed.
C) Jacques has a smaller tangential speed than George.
D) both have zero tangential speeds.
E) Cannot tell which one has the greater speed without knowing their masses.

Question 33

A dumbbell-shaped object is composed by two equal masses, m, connected by a rod of negligible mass and length r. If I₁ is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and I₂ is the moment of inertia with respect to an axis passing through one of the masses we can say that

A) I₁ = I₂.
B) I₁ > I₂.
C) I₁ < I₂.
D) There is no way to compare I₁ and I₂.

Question 34

Consider a solid sphere of radius R and mass M rolling without slipping. Which form of 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.
E) You need to know the acceleration of the sphere to tell.

Question 35

A solid sphere and a solid cylinder of the same mass and radius roll without slipping at the same 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.
D) impossible to compare to the total kinetic energy of the cylinder.

Question 36

A wheel of radius R is rolling on a horizontal surface. Its center is moving forward with speed v. A point on the wheel a distance r/3 below the center is moving forward at a speed 2v/3. The wheel is

A) rolling without slipping.
B) not rotating at all.
C) made of rubber.
D) slipping because its angular speed is too low to be rolling without slipping.
E) slipping because its angular speed is too high to be rolling without slipping.

Question 37

Two balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down an 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
B) Both reach the bottom together.
C) The large sphere
D) It depends on the height of the incline.
E) It depends on the length of the inclined surface.

Question 38

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

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

Question 39

What is the quantity used to measure an object's resistance to changes in rotational motion?

A) mass
B) moment of inertia
C) torque
D) angular velocity
E) angular acceleration

Question 40

Suppose a 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 41

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

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

Question 42

Express an angular speed of 33.3 rpm in rad/s.

Question 43

A bicycle whose wheels have a radius of 66 cm is traveling at 2.0 m/s. If the wheels do not slip, what is the angular speed of the wheels?

Question 44

A centrifuge takes 100 s to spin up from rest to its final angular speed with constant angular acceleration. A point located 8.00 cm from the axis of rotation of the centrifuge moves with a speed of 150 m/s when the centrifuge is at full speed.
(a) What is the average angular acceleration of the centrifuge as it spins up?
(b) How many revolutions does the centrifuge make as it goes from rest to its final angular speed?

Question 45

A grinding wheel is spinning at a rate of 20.0 revolutions per second. When the power to the grinder is turned off, the grinding wheel slows with constant angular acceleration and takes 80.0 s to come to a rest.
(a) What was the angular acceleration of the grinding wheel as it came to rest?
(b) How many rotations did the wheel make during the time it was coming to rest?

Question 46

What is the angular speed in rad/s of the minute hand of a clock?

Question 47

The diameter of the Moon is 3.78 × 10⁶ m. It subtends an angle of 0.00982 radians at the surface of Earth. How far is the Moon from Earth?

Question 48

A massless rod of length 1.00 m has a 2.00-kg mass attached to one end and a 3.00-kg mass attached to the other. The system rotates about a fixed axis perpendicular to the rod that passes through the rod 30.0 cm from the end with the 3.00-kg mass attached. The kinetic energy of the system is 100 J.
(a) What is the moment of inertia of this system about this axis?
(b) What is the angular speed of this system?

Question 49

A 10-m plank is being moved by rolling it over two cylindrical logs placed 2 m from either end of the plank. As the plank is pushed, the logs roll on the ground without slipping, and they do not slip with respect to the plank. How far can the plank be moved before the rear log reaches the end of the plank?

Question 50

A solid sphere of mass 1.5 kg and radius 15 cm rolls without slipping down a 35° incline that is 7.0 m long. Assume it started from rest. The moment of inertia of a sphere is given by I= (2/5)MR².
(a) Calculate the linear speed of the sphere when it reaches the bottom of the incline.
(b) Determine the angular speed of the sphere at the bottom of the incline.
(c) Does the linear speed depend on the radius or mass of the sphere?
Does the angular speed depend on the radius or mass of the sphere?

Question 51

A child is riding a merry-go-round which completes one revolution every 8.36 s. The child is standing 4.65 m from the center of the merry-go-round.
(a) What is the tangential speed of the child?
(b) What is the magnitude of the centripetal acceleration of the child?

Question 52

The Sun subtends an angle of 0.00928 radians at the surface of the earth. Its distance from Earth is 1.50 x 10¹¹ m. What is the diameter of the Sun?

Question 53

An artificial satellite in a low orbit circles the earth every 98.0 minutes. What is its angular speed in rad/s?

Question 54

How long does it take for a rotating object to speed up from 15.0 to 33.3 rad/s if it has an 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 compact disk rotates at 210 revolutions per minute. What is its angular speed in rad/s?

A) 11.0 rad/s
B) 22.0 rad/s
C) 45.3 rad/s
D) 69.1 rad/s
E) 660 rad/s

Question 56

A 10-m plank is being moved by rolling it over two cylindrical logs with a radius of 20 cm, placed 2 m from either end of the plank. As the plank is pushed, the logs roll on the ground without slipping, and they do not slip with respect to the plank. Through what angle will the logs have rotated when the plank has moved 2 m?

Question 57

Express an angle of 35.20 rad in degrees.

Question 58

A 2.00-kg solid sphere of radius 5.00 cm rolls down a 20.0° inclined plane starting from rest.
(a) What is the magnitude of the acceleration of the center of mass of the sphere?
(b) How far down the plane does it roll without slipping in 1.00 s?

Question 59

Express an angle of 450° in radians.

Question 60

A fan is turned off, and its angular speed decreases from 10.0 rad/s to 6.3 rad/s in 5.0 s. What is the magnitude of the angular acceleration of the fan?

A) 086 rad/s²
B) 0.74 rad/s²
C) 0.37 rad/s²
D) 11.6 rad/s²
E) 1.16 rad/s²

Question 61

A wheel rotates through an angle of 320° as it slows down from 78.0 rpm to 22.8 rpm. What is the magnitude of the average angular acceleration of the wheel?

A) 2.34 rad/s²
B) 5.48 rad/s²
C) 6.50 rad/s²
D) 8.35 rad/s²
E) 10.9 rad/s²

Question 62

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 63

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 64

An experiment that can be used to measure the velocity of a bullet is to have two cardboard disks attached to a rotating shaft some distance apart and to measure the angular separation of the holes made by the bullet. In such an experiment, two cardboard disks are placed 0.534 m apart on a shaft that is rotating at 3000 rpm. The bullet is fired parallel to the axis and the angular separation of the holes is measured to be 22.0°. What is the speed of the bullet?

A) 72.8 m/s
B) 139 m/s
C) 219 m/s
D) 437 m/s
E) 1380 m/s

Question 65

A child is riding a merry-go-round, which 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 angle does the acceleration of the child make with the tangential direction?

A) 90.0°
B) 25.5°
C) 32.5°
D) 64.5°
E) 45.0°

Question 66

A child is riding a tricycle. The pedals are attached directly to the front wheel, which has a radius of 13 cm. The rear wheels are smaller, and have a radius of 8.0 cm. If the child is pedaling at 16 rpm, what is the angular speed of the rear wheels?

A) 15 rpm
B) 26 rpm
C) 24 rpm
D) 20 rpm
E) 50 rpm

Question 67

A car with tires whose radius is 35 cm is traveling along a highway at 29.8 m/s. What is the angular speed of the tires?

A) 90 rad/s
B) 85 rad/s
C) 80 rad/s
D) 75 rad/s
E) 70 rad/s

Question 68

Earth's radius is 6.38 × 10⁶ m, and it completes one revolution every day. What is the tangential speed of a person standing on the equator?

A) 232 m/s
B) 148 m/s
C) 464 m/s
D) 21.5 m/s
E) 73.8 m/s

Question 69

A wheel rotates through an angle of 13.8 rad as it slows down from 22.0 rad/s to 13.5 rad/s. What is the magnitude of the average 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 70

Earth's radius is 6.38 × 10⁶ m, and it completes one revolution every day. What is the magnitude of the centripetal acceleration of a person standing on the equator?

A) 0.00844 m/s²
B) 0.00343 m/s²
C) 0.0337 m/s²
D) 0.343 m/s²
E) 0.000854 m/s²

Question 71

A potter's wheel is rotating at 1.00 rpm. What centripetal force is required to hold a 1.00 g lump of clay in place, 10.0 cm from the axis of rotation?

A) 1.10 × 10^-6 N
B) 1.20 × 10^-6 N
C) 1.30 × 10^-6 N
D) 1.40 × 10^-6 N
E) 1.50 × 10^-6 N

Question 72

A child is riding a merry-go-round, which has an instantaneous angular speed of 1.25 rad/s and an angular acceleration of 0.745 rad/ . The child is standing 4.65 m from the center of the merry-go-round. What is the magnitude of the 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 73

A Ferris wheel with a radius of 8.00 m rotates at a constant rate, completing one revolution in 30.0 s. What is the apparent weight of a 60.0-kg passenger when she is at the top of the wheel?

A) 589 N
B) 568 N
C) 615 N
D) 325 N
E) 432 N

Question 74

A child is riding a merry-go-round which completes one revolution every 8.36 s. The child is standing 4.65 m from the center of the merry-go-round. What is the magnitude of the centripetal acceleration of the child?

A) 6.84 m/s²
B) 3.94 m/s²
C) 2.63 m/s²
D) 0.0664 m/s²
E) 0.696 m/s²

Question 75

A soccer ball whose radius is 11 cm rolls a distance of 10 m in 3.50 s. What is the angular speed of the ball?

A) 5.1 m/s
B) 13 m/s
C) 26 m/s
D) 39 m/s
E) 52 m/s

Question 76

A string is wound tightly around a fixed pulley whose radius is 5.0 cm. As the string is pulled, the pulley rotates without slipping. What is the angular speed of the pulley when the string has a linear speed of 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 77

In a bicycle, the pedals drive the chainwheel, which is connected by means of a chain to the cogwheel, a small wheel attached to the rear wheel. In a certain bicycle, the radius of the chainwheel is 12.0 cm, the radius of the cogwheel is 4.0 cm, and the radius of the rear wheel is 66.0 cm. At what rate should the cyclist be pedaling in order for the bicycle to have a forward speed of 10.0 m/s?

A) 48.2 rpm
B) 16.1 rpm
C) 12.1 rpm
D) 24.1 rpm
E) 60.3 rpm

Question 78

A child is riding a merry-go-round which completes one revolution every 8.36 s. The child is standing 4.65 m from the center of the merry-go-round. What is the tangential speed of the child?

A) 5.64 m/s
B) 3.49 m/s
C) 0.556 m/s
D) 1.75 m/s
E) 1.80 m/s

Question 79

A wheel that is rotating at 33.3 rad/s is given an angular acceleration of 2.15 rad/s². Through what angle has the wheel 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 80

A Ferris wheel with a radius of 14.0 m rotates at a constant rate, completing one revolution in 30.0 s. What is the apparent weight of a 60.0-kg passenger when she is at the bottom of the wheel?

A) 589 N
B) 562 N
C) 625 N
D) 852 N
E) 432 N