Deck 8: Rotational Motion

Question 1

Choose the one alternative that best completes the statement or answers the question.
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 1

B

Question 2

Choose the one alternative that best completes the statement or answers the question.
Two forces produce equal torques on a door about the door hinge. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied
Perpendicular to the door. Which force has a greater magnitude?

A) the second force (at the doorknob)
B) the first force (at the midpoint)
C) The two forces are equal.

Answer 2

the first force (at the midpoint)

Question 3

Choose the one alternative that best completes the statement or answers the question.
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.

Answer 3

neither the mass nor the radius of the sphere.

Question 4

Choose the one alternative that best completes the statement or answers the question.
As shown in the figure, a given force is applied to a rod in several different ways. In which case is the torque about the pivot P due to this force the greatest?

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

Question 5

Choose the one alternative that best completes the statement or answers the question.
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) Both are equal.
C) Rotational kinetic energy is larger.
D) You need to know the speed of the hoop to tell.

Question 6

Choose the one alternative that best completes the statement or answers the question.
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 radial acceleration.
B) They all have the same tangential speed.
C) They all have the same angular acceleration.
D) They all have the same angular speed.
E) They all have the same tangential acceleration.

Question 7

Choose the one alternative that best completes the statement or answers the question.
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) sphere, hoop, disk
B) hoop, disk, sphere
C) sphere, disk, hoop
D) hoop, sphere, disk
E) disk, hoop, sphere

Question 8

Choose the one alternative that best completes the statement or answers the question.
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 large sphere arrives first.
B) The small sphere arrives first.
C) Both reach the bottom at the same time.

Question 9

Choose the one alternative that best completes the statement or answers the question.
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) Both are equal.
B) Translational kinetic energy is larger.
C) Rotational kinetic energy is larger.
D) You need to know the speed of the sphere to tell.

Question 10

Choose the one alternative that best completes the statement or answers the question.
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 radius of the sphere.
B) the mass of the sphere.
C) both the mass and the radius of the sphere.
D) neither the mass nor the radius of the sphere.

Question 11

Choose the one alternative that best completes the statement or answers the question.
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) cylinder
B) sphere
C) pipe
D) The pipe and cylinder arrive together before the sphere.
E) They all reach the bottom at the same time.

Question 12

Choose the one alternative that best completes the statement or answers the question.
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) less than the total kinetic energy of the cylinder.
B) more than the total kinetic energy of the cylinder.
C) equal to the total kinetic energy of the cylinder.

Question 13

Choose the one alternative that best completes the statement or answers the question.
Two equal-magnitude forces are applied to a door at the doorknob. The first force is applied perpendicular to the door, and the second force is applied at 30° to the plane of the door. Which
Force exerts the greater torque about the door hinge?

A) Both forces exert zero torque.
B) Both forces exert equal non-zero torques.
C) the first force (applied perpendicular to the door)
D) the second force (applied at an angle)

Question 14

Choose the one alternative that best completes the statement or answers the question.
A uniform ball is released from rest on a no-slip surface, as shown in the figure. After reaching its Iowest 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) at the same height from which it was released.
C) Iower than when 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 15

Choose the one alternative that best completes the statement or answers the question.
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 disk
B) The hoop
C) Both reach the bottom at the same time.

Question 16

Choose the one alternative that best completes the statement or answers the question.
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 and Ahmed have the same tangential speed.
B) Jacques has a smaller angular speed than Ahmed.
C) Ahmed has a greater tangential speed than Jacques.
D) Jacques has a greater angular speed than Ahmed.
E) Jacques and Ahmed have the same angular speed.

Question 17

Choose the one alternative that best completes the statement or answers the question.
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 greatest mass
B) the sphere
C) the one of smallest diameter
D) the disk
E) They will reach the bottom at the same time.

Question 18

Choose the one alternative that best completes the statement or answers the question.
The rotating systems shown in the figure differ only in that the two identical movable masses 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) both blocks land at the same time.
B) the block at the left lands first.
C) the block at the right lands first.

Question 19

Write the word or phrase that best completes each statement or answers the question.
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 20

Choose the one alternative that best completes the statement or answers the question.
Five forces act on a rod that is free to pivot at point P , as shown in the figure. Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice.)

A) force A
B) force B
C) force C
D) force D
E) force E

Question 21

Choose the one alternative that best completes the statement or answers the question.
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 decreases.
B) the moment of inertia of the system decreases and the angular speed remains the same.
C) the moment of inertia of the system decreases and the angular speed increases.
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 22

Choose the one alternative that best completes the statement or answers the question.
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) 4.77 s
C) 2.07 s
D) 8.26 s
E) 118 s

Question 23

Choose the one alternative that best completes the statement or answers the question.
As you are leaving a building, the door opens outward. If the hinges on the door are on your right, what is the direction of the angular velocity of the door as you open it?

A) down
B) forwards
C) to your right
D) up
E) to your left

Question 24

Choose the one alternative that best completes the statement or answers the question.
When is the angular momentum of a system constant?

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

Question 25

Choose the one alternative that best completes the statement or answers the question.
What is the angular speed, in rad/s, of a flywheel turning at 813.0 rpm?

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

Question 26

Write the word or phrase that best completes each statement or answers the question.
Express the angular speed of an old 33 1/3 rpm LP in rad/s.

Question 27

Choose the one alternative that best completes the statement or answers the question.
If the answer to your calculation has units of $\mathrm { kg } \cdot \mathrm { m } ^ { 2 } / \mathrm { s }$ what type of quantity could it be? (There could be more than one correct choice).

A) force
B) moment of inertia
C) torque
D) work
E) power
F) angular momentum
G) rotational kinetic energy
H) linear momentum

Question 28

Write the word or phrase that best completes each statement or answers the question.
An artificial satellite in a low orbit circles the earth every 98 minutes. What is its angular
speed in rad/s?

Question 29

Choose the one alternative that best completes the statement or answers the question.
Through how many degrees does a 33 rpm turntable rotate in 0.32 s?

A) $35 ^ { \circ }$
B) $46 ^ { \circ }$
C) $74 ^ { \circ }$
D) $63 ^ { \circ }$

Question 30

Choose the one alternative that best completes the statement or answers the question.
If the answer to your calculation has units of $\mathrm { kg } \cdot \mathrm { m } ^ { 2 } / \mathrm { s } ^ { 2 }$ What type pf quantity could it be? (There could be more than one correct choice.)

A) work
B) rotational kinetic energy
C) torque
D) moment of inertia
E) power
F) force
G) angular momentum
H) linear momentum

Question 31

Choose the one alternative that best completes the statement or answers the question.
A ballet dancer is spinning in the middle of a horizontal frictionless stage. Which of the following things could he change by moving parts of his body or his whole body? (There could be more than one correct choice.)

A) the horizontal component of his linear momentum
B) his translational kinetic energy
C) his angular momentum
D) his moment of inertia
E) his rotational kinetic energy
F) the location of his center of mass (or center of gravity)
G) his total kinetic energy

Question 32

Write the word or phrase that best completes each statement or answers the question.
The sun subtends an angle of 0.00928 rad when viewed from the surface of the earth, and its distance from Earth is $1.5 \times 10 ^ { 11 } \mathrm {~m}$
What is the diameter of the sun?

Question 33

Choose the one alternative that best completes the statement or answers the question.
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 increases and her angular speed remains the same.
B) her moment of inertia increases and her angular speed decreases.
C) her moment of inertia decreases and her angular speed increases.
D) her moment of inertia increases and her angular speed increases.
E) her moment of inertia decreases and her angular speed decreases.

Question 34

Choose the one alternative that best completes the statement or answers the question.
At a certain instant, a compact disc is rotating at 210 rpm. What is its angular speed in rad/s?

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

Question 35

Choose the one alternative that best completes the statement or answers the question.
A spinning ice skater on extremely smooth ice 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 kinetic energy remains constant.
B) She is subject to a constant non-zero torque.
C) Her moment of inertia remains constant.
D) Her angular momentum remains constant.

Question 36

Choose the one alternative that best completes the statement or answers the question.
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) $0,74 \mathrm { rad } / \mathrm { s } ^ { 2 }$
B) $1.2 \mathrm { rad } / \mathrm { s } ^ { 2 }$
C) $11 \mathrm { rad } / \mathrm { s } ^ { 2 }$
D) $0.37 \mathrm { rad } / \mathrm { s } ^ { 2 }$
E) $0.86 \mathrm { rad } / \mathrm { s } 2$

Question 37

Choose the one alternative that best completes the statement or answers the question.
When you ride a bicycle, in what direction is the angular velocity of the wheels?

A) up
B) to your right
C) backwards
D) to your left
E) forwards

Question 38

Write the word or phrase that best completes each statement or answers the question.
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 39

Write the word or phrase that best completes each statement or answers the question.
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 o $70 ^ { \circ } ?$

Question 40

Write the word or phrase that best completes each statement or answers the question.
The diameter of the Moon is $3.47 \times 10 ^ { 6 } \mathrm {~m}$ and it subtends an angle of 0.00904 rad when viewed from the surface of Earth. How far is the Moon from Earth?

Question 41

Choose the one alternative that best completes the statement or answers the question.
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 $3.45 \mathrm { rad } / \mathrm { s } ^ { 2 } ?$

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

Question 42

Choose the one alternative that best completes the statement or answers the question.
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) 50 rad/s
B) 10 rad/s
C) 25 rad/s
D) 100 rad/s
E) 20 rad/s

Question 43

Write the word or phrase that best completes each statement or answers the question.
A wheel accelerates with a constant angular acceleration of $4.5 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 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 anqular speed at that time?

Question 44

Choose the one alternative that best completes the statement or answers the question.
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) $0.90 \mathrm { rad } / \mathrm { s } ^ { 2 }$
B) $5.7 \mathrm { rad } / \mathrm { s } ^ { 2 }$
C) $11 \mathrm { rad } / \mathrm { s } ^ { 2 }$
D) $1.8 \mathrm { rad } / \mathrm { s } ^ { 2 }$

Question 45

Choose the one alternative that best completes the statement or answers the question.
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) 100 rpm
B) 955 rpm
C) 50.0 rpm
D) 47.7 rpm
E) 72.0 rpm

Question 46

Choose the one alternative that best completes the statement or answers the question.
An electrical motor spins at a constant 2695.0 rpm. If the rotor radius is 7.165 cm, what is the linear acceleration of the edge of the rotor?

A) $28.20 \mathrm {~m} / \mathrm { s } ^ { 2 }$
B) $281.6 \mathrm {~m} / \mathrm { s } ^ { 2 }$
C) $5707 \mathrm {~m} / \mathrm { s } ^ { 2 }$
D) $572,400 \mathrm {~m} / \mathrm { s } 2$

Question 47

Write the word or phrase that best completes each statement or answers the question.
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 48

Choose the one alternative that best completes the statement or answers the question.
A wheel accelerates from rest to 59 rad/s at a uniform rate of $58 \mathrm { rad } / \mathrm { s } ^ { 2 }$ Through what angle (in radians) did the wheel turn while accelerating?

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

Question 49

Write the word or phrase that best completes each statement or answers the question.
A wheel starts from rest and has a uniform angular acceleration of $4.0 \mathrm { rad } / \mathrm { s } ^ { 2 }$
After the wheel completes its first revolution, how long does it take for it to make its second complete revolution?

Question 50

Choose the one alternative that best completes the statement or answers the question.
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 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 $1.5 \mathrm { rad } / \mathrm { s } ^ { 2 }$ until the wheel stops. For how long a time after the power is shut off does it take the wheel to stop?

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

Question 51

Choose the one alternative that best completes the statement or answers the question.
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 38 rad/s . The wheel is run
at that angular speed for 30 s and then power is shut off. The wheel slows down uniformly at
$2.1 \mathrm { rad } / \mathrm { s } ^ { 2 }$
between t=0 s and t=10 s ?

A) $6.1 \mathrm { rad } / \mathrm { s } ^ { 2 }$
B) $5.3 \mathrm { rad } / \mathrm { s } ^ { 2 }$
C) $6.8 \mathrm { rad } / \mathrm { s } ^ { 2 }$
D) $3.8 \mathrm { rad } / \mathrm { s } ^ { 2 }$
E) $4.6 \mathrm { rad } / \mathrm { s } ^ { 2 }$

Question 52

Choose the one alternative that best completes the statement or answers the question.
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) 7.6 rad/s
C) 13 rad/s
D) 0.36 rad/s
E) 4.8 rad/s

Question 53

Write the word or phrase that best completes each statement or answers the question.
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 $0.010 \mathrm { rad } / \mathrm { s } 2$ 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 54

Write the word or phrase that best completes each statement or answers the question.
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 55

Choose the one alternative that best completes the statement or answers the question.
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 58 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 $1.4 \mathrm { rad } / \mathrm { s } ^ { 2 }$ until the wheel stops. What is the total number of revolutions made by the wheel in this situation?

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

Question 56

Choose the one alternative that best completes the statement or answers the question.
A child is riding a merry-go-round that has an instantaneous angular speed of 1.25 rad/s and an angular acceleration o $0.745 \mathrm { rad } / \mathrm { s } ^ { 2 }$ 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) $2.58 \mathrm {~m} / \mathrm { s } ^ { 2 }$
B) $4.10 \mathrm {~m} / \mathrm { s } ^ { 2 }$
C) $8.05 \mathrm {~m} / \mathrm { s } ^ { 2 }$
D) $3.46 \mathrm {~m} / \mathrm { s } ^ { 2 }$
E) $7.27 \mathrm {~m} / \mathrm { s } ^ { 2 }$

Question 57

Write the word or phrase that best completes each statement or answers the question.
When an old LP turntable was revolving at $33 \frac { 1 } { 3 } \mathrm { rpm }$ it was shut off and uniformly
slowed down and stopped in 5.5 seconds.
(a) What was the magnitude of its angular acceleration $\left( \text { in } \mathrm { rad } / \mathrm { s } ^ { 2 } \right)$
as it slowed down?
(b) Through how many revolutions did it turn while stopping?

Question 58

Write the word or phrase that best completes each statement or answers the question.
A bicycle wheel has an initial angular speed of 7.2 rad/s. After turning through one-half 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 one-half revolution?

Question 59

Write the word or phrase that best completes each statement or answers the question.
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 60

Choose the one alternative that best completes the statement or answers the question.
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) 3.50 m/s
B) 1.75 m/s
C) 1.80 m/s
D) 0.556 m/s
E) 5.64 m/s

Question 61

Choose the one alternative that best completes the statement or answers the question.
A triatomic molecule is oriented as follows along the x -axis: mass m is at the origin, mass 2 m is at x=a , and, mass 3 m is at x=2 a . What is the moment of inertia of this molecule about the y -axis?

A) $3 m a ^ { 2 }$
B) $14 m a ^ { 2 }$
C) $2 m a ^ { 2 }$
D) $12 m a ^ { 2 }$

Question 62

Write the word or phrase that best completes each statement or answers the question.
The L-shaped object shown in the figure consists of three small masses connected by thi 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 63

Choose the one alternative that best completes the statement or answers the question.
A Ferris wheel rotating at 20 rad/s slows down with a constant angular acceleration of magnitude $5.0 \mathrm { rad } / \mathrm { s } ^ { 2 }$
How many revolutions does it make while slowing down before coming to rest?

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

Question 64

Write the word or phrase that best completes each statement or answers the question.
In the figure, a weightlifter's barbell consists of two identical small but dense spherical
weights, each of mass 50 kg. These weights 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 weights are small enough to be treated as point
masses.

Question 65

Write the word or phrase that best completes each statement or answers the question.
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 66

Choose the one alternative that best completes the statement or answers the question.
To drive a typical car at 40 mph on a level road for one hour requires about $3.2 \times 10 ^ { 7 } \mathrm {~J}$ 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 $3.2 \times 10 ^ { 7 } \mathrm {~J} ?$

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

Question 67

Write the word or phrase that best completes each statement or answers the question.
The L-shaped object shown in the figure consists of three small masses 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 68

Write the word or phrase that best completes each statement or answers the question.
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 69

Write the word or phrase that best completes each statement or answers the question.
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 200 rev/s. Assuming all of this stored kinetic energy could be transferred to the linear speed of the 1500-kg car, find the maximum attainable speed of the car.

Question 70

Choose the one alternative that best completes the statement or answers the question.
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) 2.
B) 4.
C) 4/5.
D) 8/5.
E) 1/2.

Question 71

Choose the one alternative that best completes the statement or answers the question.
A potter's wheel has the shape of a solid uniform disk of mass 7.0 kg 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) $2.5 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$
B) $1.5 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$
C) $1.8 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$
D) $0.40 \mathrm {~kg} \cdot \mathrm { m } ^ { 2 }$

Question 72

Write the word or phrase that best completes each statement or answers the question.
The L-shaped object shown in the figure consists of three small masses 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 73

Choose the one alternative that best completes the statement or answers the question.
An old 78 rpm record rotates through an angle of $320 ^ { \circ }$ 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) $5.46 \mathrm { rad } / \mathrm { s } ^ { 2 }$
B) $2.34 \mathrm { rad } / \mathrm { s } ^ { 2 }$
C) $10.9 \mathrm { rad } / \mathrm { s } 2$
D) $8.35 \mathrm { rad } / \mathrm { s } ^ { 2 }$
E) $6.50 \mathrm { rad } / \mathrm { s } ^ { 2 }$

Question 74

Choose the one alternative that best completes the statement or answers the question.
A pulley has an initial angular speed of 12.5 rad/s and a constant angular acceleration of 3.41 $\mathrm { rad } / \mathrm { s } ^ { 2 }$ Through what angle does the pulley turn in 5.26 s?

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

Question 75

Write the word or phrase that best completes each statement or answers the question.
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 76

Choose the one alternative that best completes the statement or answers the question.
An old LP record that is originally rotating at 33.3 rad/s is given 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) 66.8 rad
B) 316 rad
C) 83.2 rad
D) 697 rad
E) 948 rad

Question 77

Write the word or phrase that best completes each statement or answers the question.
The L-shaped object shown in the figure consists of three small masses 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 78

Choose the one alternative that best completes the statement or answers the question.
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) 0.700 J
B) 0.960 J
C) 0.350 J
D) 2.10 J
E) 4.20 J

Question 79

Choose the one alternative that best completes the statement or answers the question.
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) $0.616 \mathrm { rad } / \mathrm { s } ^ { 2 }$
B) $5.45 \mathrm { rad } / \mathrm { s } ^ { 2 }$
C) $22.5 \mathrm { rad } / \mathrm { s } ^ { 2 }$
D) $10.9 \mathrm { rad } / \mathrm { s } 2$
E) $111 \mathrm { rad } / \mathrm { s } 2$

Question 80

Choose the one alternative that best completes the statement or answers the question.
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) 1.1 J
B) 0.092 J
C) 0.18 J
D) 17 J
E) 0.96 J