1. A uniform 13-kg trap door is oriented horizontally and hinged as shown. What is the magnitude of the torque on the door at the instant that the release is activated and the door can freely rotate?

A.4.9 N • m
B.9.8 N • m
C.48 N • m
D.72 N • m
E.96 N • m


2. In this drawing, the large wheel has a radius of 8.5 m. A rope is wrapped around the edge of the wheel and a 7.6 kg-box hangs from the rope. A smaller disk of radius 1.9 m is attached to the wheel. A rope is wrapped around the edge of the disk as shown. An axis of rotation passes through the center of the wheel-disk system. What is the value of the mass M that will prevent the wheel from rotating?

A.1.7 kg
B.3.8 kg
C.12 kg
D.34 kg
E.46 kg


3. A 50 N • m torque acts on a wheel of moment of inertia 150 kg • m2. If the wheel starts from rest, how long will it take the wheel to make one revolution?
A.0.33 s
B.0.66 s
C.2.4 s
D.6.1 s
E.10 s


4. A certain merry-go-round is accelerated uniformly from rest and attains an angular speed of 0.4 rad/s in the first 10 seconds. If the net applied torque is 2000 N • m, what is the moment of inertia of the merry-go-round?
A.400 kg • m2
B.800 kg • m2
C.5000 kg • m2
D.50 000 kg • m2
E.This cannot be determined since the radius is not specified.


5. Which one of the following statements concerning the moment of inertia I is false?
A.I may be expressed in units of kg • m2.
B.I depends on the angular acceleration of the object as it rotates.
C.I depends on the location of the rotation axis relative to the particles that make up the object.
D.I depends on the orientation of the rotation axis relative to the particles that make up the object.
E.Of the particles that make up an object, the particle with the smallest mass may contribute the greatest amount to I.


6. A hollow cylinder of mass M and radius R rolls down an inclined plane. A block of mass M slides down an identical inclined plane. If both objects are released at the same time,
A.the cylinder will reach the bottom first.
B.the block will reach the bottom first.
C.the block will reach the bottom with the greater kinetic energy.
D.the cylinder will reach the bottom with the greater kinetic energy.
E.both the block and the cylinder will reach the bottom at the same time.


7. A 1.0-kg wheel in the form of a solid disk rolls along a horizontal surface with a speed of 6.0 m/s. What is the total kinetic energy of the wheel?
A.9.0 J
B.18 J
C.27 J
D.36 J
E.54 J


8. A 2.0-kg solid cylinder of radius 0.5 m rotates at a rate of 40 rad/s about its cylindrical axis. What power is required to bring the cylinder to rest in 10 s?
A.20 W
B.40 W
C.160 W
D.200 W
E.400 W


9. A child standing on the edge of a freely spinning merry-go-round moves quickly to the center. Which one of the following statements is necessarily true concerning this event and why?
A.The angular speed of the system decreases because the moment of inertia of the system has increased.
B.The angular speed of the system increases because the moment of inertia of the system has increased.
C.The angular speed of the system decreases because the moment of inertia of the system has decreased.
D.The angular speed of the system increases because the moment of inertia of the system has decreased.
E.The angular speed of the system remains the same because the net torque on the merry-go-round is zero newton • meters.


10. A spinning skater draws in her outstretched arms thereby reducing her moment of inertia by a factor of 2. Determine the ratio of her final kinetic energy to her initial kinetic energy.
A.0.5
B.1
C.2
D.4
E.16


11. Two equal spheres, labeled A and B in the figure, are attached to a massless rod with a frictionless pivot at the point P. The system is made to rotate clockwise with angular speed w on a horizontal, frictionless tabletop. Sphere A collides with and sticks to another sphere of which is at rest on the tabletop. Note: the masses of all three spheres are equal. What is the angular speed of the system immediately after the collision?

A.w
B.0.82w
C.0.60w
D.0.56w
E.0.29w


12. A ball of mass M moves in a circular path on a horizontal, frictionless surface. It is attached to a light string that passes through a hole in the center of the table. If the string is pulled down, thereby reducing the radius of the ball's path, the speed of the ball is observed to increase. Complete the following sentence: This occurs because

A.the linear momentum of the ball is conserved.
B.it is required by Newton's first law of motion.
C.the angular momentum of the ball is conserved.
D.the angular momentum of the ball must increase.
E.the total mechanical energy of the ball must remain constant.


13. A 3.0-kg ball moves in a straight line at 10 m/s as shown in the figure. At the instant shown, what is its angular momentum about the point P?

A.30 kg • m2/s
B.90 kg • m2/s
C.120 kg • m2/s
D.150 kg • m2/s
E.zero kg • m2/s


14.
Two skaters, each of mass 40 kg, approach each other along parallel paths that are separated by a distance of 2 m. Both skaters have a speed of 10 m/s.
The first skater carries a 2-m pole that may be considered massless. As he passes the pole, the second skater catches hold of the end. The two skaters then go around in a circle about the center of the pole.
R-1 Ref 9-2

What is the angular speed of the skaters after they have linked together?
A.4 rad/s
B.5 rad/s
C.10 rad/s
D.20 rad/s
E.40 rad/s



15.
Two skaters, each of mass 40 kg, approach each other along parallel paths that are separated by a distance of 2 m. Both skaters have a speed of 10 m/s.
The first skater carries a 2-m pole that may be considered massless. As he passes the pole, the second skater catches hold of the end. The two skaters then go around in a circle about the center of the pole.
R-1 Ref 9-2

What is their combined angular momentum about the center of the pole?
A.2 kg • m2/s
B.40 kg • m2/s
C.80 kg • m2/s
D.400 kg • m2/s
E.800 kg • m2/s



16.
A 2.0-kg hoop rolls without slipping on a horizontal surface so that its center proceeds to the right with a constant linear speed of 6.0 m/s.
R-2 Ref 9-3

Which one of the following statements is true concerning the angular momentum of this hoop?
A.It points into the paper.
B.It points out of the paper.
C.It points to the left.
D.It points to the right.
E.It varies from point to point on the hoop.



17. A steady horizontal force F of magnitude 21 N is applied at the axle of a solid disk as shown. The disk has mass 2.0 kg and diameter 0.10 m. What is the linear speed of the center of the disk after it has moved 12 m?

A.9.0 m/s
B.13 m/s
C.18 m/s
D.40 m/s
E.80 m/s


18. A uniform disk of radius 1.2 m and mass 0.60 kg is rotating at 25 rad/s around an axis that passes through its center and is perpendicular to the disk. A rod makes contact with the rotating disk with a force of 4.5 N at a point 0.75 m from the axis of rotation as shown. The disk is brought to a stop in 5.0 s. What is the coefficient of kinetic friction for the two materials in contact?

A.0.22
B.0.15
C.0.64
D.0.37
E.0.55



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