Question 1

In the figure, point P is at rest when it is on the x-axis. The time t, when P returns to the original position on the x-axis, is closest to

Accepted Answer

A)  13 s. 
B)  18 s. 
C)  25 s. 
D)  35 s. 
E)  50 s. 
A)  13 s. 
B)  18 s. 
C)  25 s. 
D)  35 s. 
E)  50 s. D

Question 2

A stepladder consists of two halves, hinged at the top, and connected by a tie rod that keeps the two halves from spreading apart. In this particular instance, the two halves are 2.50 m long, the tie rod is connected to the center of each half and is 70.0 cm long. An 800-N person stands 3/5 of the way up the stepladder, as shown in the figure. Neglecting the weight of the ladder, and assuming that the ladder is resting on a smooth floor, what is the tension in the tie rod? Note: To solve this problem you must "cut" the ladder in half and consider the equilibrium of forces and torques acting on each half of the ladder.

Accepted Answer

A)  140 N 
B)  240 N 
C)  280 N 
D)  360 N 
E)  560 N 
A)  140 N 
B)  240 N 
C)  280 N 
D)  360 N 
E)  560 N A

Question 3

A long thin rod of length L has a linear density λ(x) = Ax where x is the distance from the left end of the rod.
(a) How far is the center of mass of the rod from the left end of the rod?
(b) What is the mass of the rod?

Accepted Answer

(a) 2L/3 (b) AL²/2

Question 4

A 95 N force exerted at the end of a   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?

Accepted Answer

A)  18° 
B)  14° 
C)  22° 
D)  25° 
A)  18° 
B)  14° 
C)  22° 
D)  25°

Question 5

A uniform solid sphere of mass M and radius R rotates with an angular speed ω about an axis through its center. A uniform solid cylinder of mass M, radius R, and length 2R rotates through an axis running through the central axis of the cylinder. What must be the angular speed of the cylinder so it will have the same rotational kinetic energy as the sphere?

Accepted Answer

A)  2ω/5 
B)    ω 
C)  4ω/5 
D)  2ω/   
E)  ω/   
A)  2ω/5 
B)    ω 
C)  4ω/5 
D)  2ω/   
E)  ω/

Question 6

A horizontal disk rotates about a vertical axis through its center. Point P is midway between the center and the rim of the disk, and point Q is on the rim. If the disk turns with constant angular velocity, which of the following statements about it are true? (There may be more than one correct choice.)

Accepted Answer

A)  P and Q have the same linear acceleration. 
B)  Q is moving twice as fast as P. 
C)  The linear acceleration of Q is twice as great as the linear acceleration of P. 
D)  The linear acceleration of P is twice as great as the linear acceleration of Q. 
E)  The angular velocity of Q is twice as great as the angular velocity of P. 
A)  P and Q have the same linear acceleration. 
B)  Q is moving twice as fast as P. 
C)  The linear acceleration of Q is twice as great as the linear acceleration of P. 
D)  The linear acceleration of P is twice as great as the linear acceleration of Q. 
E)  The angular velocity of Q is twice as great as the angular velocity of P.

Question 7

A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii and are of uniform density. If the three are released simultaneously at the top of an inclined plane and roll without slipping, which one will reach the bottom first?

Accepted Answer

A)  solid sphere 
B)  hollow pipe 
C)  solid cylinder 
D)  They all reach the bottom at the same time. 
A)  solid sphere 
B)  hollow pipe 
C)  solid cylinder 
D)  They all reach the bottom at the same time.

Question 8

The two rotating systems shown in the figure differ only in that the two identical movable masses are positioned at different distances from the axis of rotation. If you release the hanging blocks simultaneously from rest, and if the ropes do not slip, which block lands first?

Accepted Answer

A)  The block at the left lands first. 
B)  The block at the right lands first. 
C)  Both blocks land at the same time. 
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 9

A uniform solid cylinder of radius R and a thin uniform spherical shell of radius R both roll without slipping. If both objects have the same mass and the same kinetic energy, what is the ratio of the linear speed of the cylinder to the linear speed of the spherical shell?

Accepted Answer

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

Question 10

A futuristic design for a car is to have a large solid disk-shaped flywheel within the car storing kinetic energy. The uniform flywheel has mass 370 kg with a radius of 0.500 m and can rotate up to   Assuming all of this stored kinetic energy could be transferred to the linear velocity of the   car, find the maximum attainable speed of the car.

Accepted Answer

The answer of A futuristic design for a car is...

Question 11

At any angular speed, a certain uniform solid sphere of diameter D has half as much rotational kinetic energy as a certain uniform thin-walled hollow sphere of the same diameter when both are spinning about an axis through their centers. If the mass of the solid sphere is M, the mass of the hollow sphere is

Accepted Answer

A)  3/5 M. 
B)  5/3 M. 
C)  5/6 M. 
D)  6/5 M. 
E)  2 M. 
A)  3/5 M. 
B)  5/3 M. 
C)  5/6 M. 
D)  6/5 M. 
E)  2 M.

Question 12

A very thin uniform rod, 2.40 m long and of weight 135 N, has a frictionless hinge at its lower end. It starts out vertically from rest and falls, pivoting about the hinge. Just as it has rotated through an angle of 55.0°, what is the downward acceleration of the end farthest from the hinge?

Accepted Answer

A)  5.02 m/s2 
B)  8.03 m/s2 
C)  9.80 m/s2 
D)  12.0 m/s2 
E)  19.6 m/s2 
A)  5.02 m/s2 
B)  8.03 m/s2 
C)  9.80 m/s2 
D)  12.0 m/s2 
E)  19.6 m/s2

Question 13

A 2.00-m rod of negligible mass connects two very small objects at its ends. The mass of one object is 1.00 kg and the mass of the other is unknown. The center of mass of this system is on the rod a distance 1.60 m from the 1.00-kg mass object. What is the mass of the other object?

Accepted Answer

A)  4.11 kg 
B)  3.22 kg 
C)  4.00 kg 
D)  0.250 kg 
E)  0.800 kg 
A)  4.11 kg 
B)  3.22 kg 
C)  4.00 kg 
D)  0.250 kg 
E)  0.800 kg

Question 14

While spinning down from 500.0 rpm to rest, a solid uniform flywheel does   of work. If the radius of the disk is   what is its mass?

Accepted Answer

A)  5.2 kg 
B)  4.4 kg 
C)  6.0 kg 
D)  6.8 kg 
A)  5.2 kg 
B)  4.4 kg 
C)  6.0 kg 
D)  6.8 kg

Question 15

A solid uniform brick is placed on a sheet of wood. When one end of the sheet is raised (see figure), you observe that the maximum that the angle θ can be without tipping over the brick is 49.6°. There is enough friction to prevent the brick from sliding. What is the width w of the brick?

Accepted Answer

A)  5.18 cm 
B)  6.09 cm 
C)  6.81 cm 
D)  9.40 cm 
E)  10.5 cm 
A)  5.18 cm 
B)  6.09 cm 
C)  6.81 cm 
D)  9.40 cm 
E)  10.5 cm

Question 16

A 4.50-kg wheel that is 34.5 cm in diameter 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?

Accepted Answer

A)  0.616 rad/s2 
B)  5.45 rad/s2 
C)  111 rad/s2 
D)  22.5 rad/s2 
E)  10.9 rad/s2 
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 17

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?

Accepted Answer

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

Question 18

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), its velocity with respect to the road is

Accepted Answer

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

Question 19

If   and   are nonzero vectors for which   ∙   = 0, it must follow that

Accepted Answer

A)    ×   = 0. 
B)    is parallel to   . 
C)  |   ×   | = AB. 
D)  |   ×   | = 1. 
A)    ×   = 0. 
B)    is parallel to   . 
C)  |   ×   | = AB. 
D)  |   ×   | = 1.

Question 20

A bicycle wheel of radius 0.36 m and mass 3.2 kg is set spinning at 4.00 rev/s. A very light bolt is attached to extend the axle in length, and a string is attached to the axle at a distance of 0.10 m from the wheel. Initially the axle of the spinning wheel is horizontal, and the wheel is suspended only from the string. We can ignore the mass of the axle and spokes. At what rate will the wheel process about the vertical?

Accepted Answer

A)  2.9 rpm 
B)  1.9 rpm 
C)  18 rpm 
D)  0.30 rpm 
E)  0.77 rpm 
A)  2.9 rpm 
B)  1.9 rpm 
C)  18 rpm 
D)  0.30 rpm 
E)  0.77 rpm

Exam 12: Rotation of a Rigid Body

In the figure, point P is at rest when it is on the x-axis. The time t, when P returns to the original position on the x-axis, is closest to

A long thin rod of length L has a linear density λ(x) = Ax where x is the distance from the left end of the rod. (a) How far is the center of mass of the rod from the left end of the rod? (b) What is the mass of the rod?

A 95 N force exerted at the end of a 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 solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii and are of uniform density. If the three are released simultaneously at the top of an inclined plane and roll without slipping, which one will reach the bottom first?

The two rotating systems shown in the figure differ only in that the two identical movable masses are positioned at different distances from the axis of rotation. If you release the hanging blocks simultaneously from rest, and if the ropes do not slip, which block lands first?

A uniform solid cylinder of radius R and a thin uniform spherical shell of radius R both roll without slipping. If both objects have the same mass and the same kinetic energy, what is the ratio of the linear speed of the cylinder to the linear speed of the spherical shell?

A very thin uniform rod, 2.40 m long and of weight 135 N, has a frictionless hinge at its lower end. It starts out vertically from rest and falls, pivoting about the hinge. Just as it has rotated through an angle of 55.0°, what is the downward acceleration of the end farthest from the hinge?

A 2.00-m rod of negligible mass connects two very small objects at its ends. The mass of one object is 1.00 kg and the mass of the other is unknown. The center of mass of this system is on the rod a distance 1.60 m from the 1.00-kg mass object. What is the mass of the other object?

While spinning down from 500.0 rpm to rest, a solid uniform flywheel does of work. If the radius of the disk is what is its mass?

A solid uniform brick is placed on a sheet of wood. When one end of the sheet is raised (see figure), you observe that the maximum that the angle θ can be without tipping over the brick is 49.6°. There is enough friction to prevent the brick from sliding. What is the width w of the brick?

A 4.50-kg wheel that is 34.5 cm in diameter 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?

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 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), its velocity with respect to the road is

If and are nonzero vectors for which ∙ = 0, it must follow that

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A 95 N force exerted at the end of a 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?