Name: ___________________________________    Date: ______________



1.
Two uniform cylinders have different masses and different rotational inertias. They simultaneously start from rest at the top of an inclined plane and roll without sliding down the plane. The cylinder that gets to the bottom first is:
A.
the one with the larger mass
B.
the one with the smaller mass
C.
the one with the larger rotational inertia
D.
the one with the smaller rotational inertia
E.
neither (they arrive together)


2.
Two identical disks, with rotational inertia I (= 1/2 MR2), roll without slipping with the same initial speed across a horizontal floor and then up inclines. Disk A rolls up its incline without sliding. On the other hand, disk B rolls up a frictionless incline. Otherwise the inclines are identical. Disk A reaches a height 12 cm above the floor before rolling down again. Disk B reaches a height above the floor of:
A.
24 cm
B.
18 cm
C.
12 cm
D.
8 cm
E.
6 cm


3.
A single force acts on a particle situated on the positive x axis. The torque about the origin is in the negative z direction. The force might be:
A.
in the positive y direction
B.
in the negative y direction
C.
in the positive x direction
D.
in the negative x direction
E.
in the positive z direction


4.
A uniform disk, a thin hoop, and a uniform sphere, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center. Assume the hoop is connected to the rotation axis by light spokes. With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown. Rank the objects according to their angular momenta after a given time t, least to greatest.
A.
all tie
B.
disk, hoop, sphere
C.
hoop, disk, sphere
D.
hoop, sphere, disk


5.
A single force acts on a particle P. Rank each of the orientations of the force shown below according to the magnitude of the time rate of change of the particle's angular momentum about the point O, least to greatest.
A.
1, 2, 3, 4
B.
1 and 2 tie, then 3, 4
C.
1 and 2 tie, then 4, 3
D.
1 and 2 tie, then 3 and 4 tie
E.
All are the same


6.
An ice skater with rotational inertia I0 is spinning with angular speed ω 0. She pulls her arms in, thereby increasing her angular speed to 4ω 0. Her rotational inertia is then:
A.
I0
B.
I0 /2
C.
2 I0
D.
I0 /4
E.
4 I0


7.
A man, with his arms at his sides, is spinning on a light frictionless turntable. When he extends his arms:
A.
his angular velocity increases
B.
his angular velocity remains the same
C.
his rotational inertia decreases
D.
his rotational kinetic energy increases
E.
his angular momentum remains the same


8.
When a man on a frictionless rotating stool extends his arms horizontally, his rotational kinetic energy:
A.
must increase
B.
must decrease
C.
must remain the same
D.
may increase or decrease depending on his initial angular velocity
E.
may increase or decrease depending on his angualar acceleration


9.
When a woman on a frictionless rotating turntable extends her arms out horizontally, her angular momentum:
A.
must increase
B.
must decrease
C.
must remain the same
D.
may increase or decrease depending on her initial angular velocity
E.
tilts away from the vertical


10.
A phonograph record is dropped onto a freely spinning turntable. Then:
A.
neither angular momentum nor mechanical energy is conserved because of the frictional forces between record and turntable
B.
the frictional force between record and turntable increases the total angular momentum
C.
the frictional force between record and turntable decreases the total angular momentum
D.
the total angular momentum remains constant
E.
the sum of the angular momentum and rotational kinetic energy remains constant


11.
Two pendulum bobs of unequal mass are suspended from the same fixed point by strings of equal length. The lighter bob is drawn aside and then released so that it collides with the other bob on reaching the vertical position. The collision is elastic. What quantities are conserved in the collision?
A.
Both kinetic energy and angular momentum of the system
B.
Only kinetic energy
C.
Only angular momentum
D.
Angular speed of lighter bob
E.
None of the above


12.
A particle, held by a string whose other end is attached to a fixed point C, moves in a circle on a horizontal frictionless surface. If the string is cut, the angular momentum of the particle about the point C:
A.
increases
B.
decreases
C.
does not change
D.
changes direction but not magnitude
E.
none of these


13.
A block with mass M, on the end of a string, moves in a circle on a horizontal frictionless table as shown. As the string is slowly pulled through a small hole in the table:
A.
the angular momentum of M remains constant
B.
the angular momentum of M decreases
C.
the kinetic energy of M remains constant
D.
the kinetic energy of M decreases
E.
none of the above


14.
A meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark. A force is applied perpendicularly to the end of the stick at 0 cm, as shown. A second force (not shown) is applied perpendicularly at the 60-cm mark. The forces are horizontal. If the stick does not move, the force exerted by the pivot on the stick:
A.
must be zero
B.
must be in the same direction as and have magnitude
C.
must be directed opposite to and have magnitude
D.
must be in the same direction as and have magnitude
E.
must be directed opposite to and have magnitude


15.
The diagram shows a stationary 5-kg uniform rod (AC), 1 m long, held against a wall by a rope (AE) and friction between the rod and the wall. To use a single equation to find the force exerted on the rod by the rope at which point should you place the reference point for computing torque?
A.
A
B.
B
C.
C
D.
D
E.
E


16.
A uniform rod AB is 1.2 m long and weighs 16 N. It is suspended by strings AC and BD as shown. A block P weighing 96 N is attached at E, 0.30 m from A. The magnitude of the tension force in the string BD is:
A.
8.0 N
B.
24 N
C.
32 N
D.
48 N
E.
80 N


17.
An 800-N man stands halfway up a 5.0 m ladder of negligible weight. The base of the ladder is 3.0 m from the wall as shown. Assuming that the wall-ladder contact is frictionless, the wall pushes against the ladder with a force of:
A.
150 N
B.
300 N
C.
400 N
D.
600 N
E.
800 N


18.
A uniform ladder is 10 cm long and weighs 400 N. It rests with its upper end against a frictionless vertical wall. Its lower end rests on the ground and is prevented from slipping by a peg driven into the ground. The ladder makes a 30° angle with the horizontal. The force exerted on the wall by the ladder is:
A.
48 N
B.
74 N
C.
120 N
D.
350 N
E.
610 N


19.
The 600-N ball shown is suspended on a string AB and rests against the frictionless vertical wall. The string makes an angle of 30° with the wall. The magnitude of the tension for of string is:
A.
690 N
B.
1200 N
C.
2100 N
D.
2400 N
E.
none of these


20.
The 600-N ball shown is suspended on a string AB and rests against the frictionless vertical wall. The string makes an angle of 30° with the wall. The ball presses against the wall with a force of magnitude:
A.
120 N
B.
300 N
C.
350 N
D.
600 N
E.
690 N


21.
A horizontal beam of weight W is supported by a hinge and cable as shown. The force exerted on the beam by the hinge has a vertical component that must be:
A.
nonzero and up
B.
nonzero and down
C.
nonzero but not enough information given to know whether up or down
D.
zero
E.
equal to W


22.
An oscillatory motion must be simple harmonic if:
A.
the amplitude is small
B.
the potential energy is equal to the kinetic energy
C.
the motion is along the arc of a circle
D.
the acceleration varies sinusoidally with time
E.
the derivative, dU/dx, of the potential energy is negative


23.
In simple harmonic motion, the magnitude of the acceleration is:
A.
constant
B.
proportional to the displacement
C.
inversely proportional to the displacement
D.
greatest when the velocity is greatest
E.
never greater than g


24.
In simple harmonic motion, the magnitude of the acceleration is greatest when:
A.
the displacement is zero
B.
the displacement is maximum
C.
the speed is maximum
D.
the force is zero
E.
the speed is between zero and its maximum


25.
In simple harmonic motion, the displacement is maximum when the:
A.
acceleration is zero
B.
velocity is maximum
C.
velocity is zero
D.
kinetic energy is maximum
E.
momentum is maximum


26.
In simple harmonic motion:
A.
the acceleration is greatest at the maximum displacement
B.
the velocity is greatest at the maximum displacement
C.
the period depends on the amplitude
D.
the acceleration is constant
E.
the acceleration is greatest at zero displacement


27.
The amplitude and phase constant of an oscillator are determined by:
A.
the frequency
B.
the angular frequency
C.
the initial displacement alone
D.
the initial velocity alone
E.
both the initial displacement and velocity


28.
In simple harmonic motion, the restoring force must be proportional to the:
A.
amplitude
B.
frequency
C.
velocity
D.
displacement
E.
displacement squared


29.
An object of mass m, oscillating on the end of a spring with spring constant k has amplitude A. Its maximum speed is:
A.
B.
A2k/m
C.
D.
Am/k
E.
A2m/k


30.
The amplitude of oscillation of a simple pendulum is increased from 1° to 4°. Its maximum acceleration changes by a factor of:
A.
1/4
B.
1/2
C.
2
D.
4
E.
16


31.
A simple pendulum of length L and mass M has frequency f. To increase its frequency to 2f:
A.
increase its length by length to 4L
B.
increase its length by length to 2L
C.
decrease its length by length to L/2
D.
decrease its length by length to L/ 4
E.
decrease its mass by length to < M/4


32.
A simple pendulum has length L and period T. As it passes through its equilibrium position, the string is suddenly clamped at its mid-point. The period then becomes:
A.
2T
B.
T
C.
T/2
D.
T/4
E.
none of the above


33.
A simple pendulum is suspended from the ceiling of an elevator. The elevator is accelerating upwards with acceleration a. The period of this pendulum, in terms of its length L, g and a is:
A.
B.
C.
D.
E.


34.
Five hoops are each pivoted at a point on the rim and allowed to swing as physical pendulums. The masses and radii are
 
hoop 1: M = 150g and R = 50 cm
 
hoop 2: M = 200g and R = 40 cm
 
hoop 3: M = 250g and R = 30 cm
 
hoop 4: M = 300g and R = 20 cm
 
hoop 5: M = 350g and R = 10 cm
Order the hoops according to the periods of their motions, smallest to largest.
A.
1, 2, 3, 4, 5
B.
5, 4, 3, 2, 1
C.
1, 2, 3, 5, 4
D.
1, 2, 5, 4, 3
E.
5, 4, 1, 2, 3


35.
The rotational inertia of a uniform thin rod about its end is ML2/3, where M is the mass and L is the length. Such a rod is hung vertically from one end and set into small amplitude oscillation. If L = 1.0 m this rod will have the same period as a simple pendulum of length:
A.
33 cm
B.
50 cm
C.
67 cm
D.
100 cm
E.
150 cm


36.
A sinusoidal force with a given amplitude is applied to an oscillator. To maintain the largest amplitude oscillation the frequency of the applied force should be:
A.
half the natural frequency of the oscillator
B.
the same as the natural frequency of the oscillator
C.
twice the natural frequency of the oscillator
D.
unrelated to the natural frequency of the oscillator
E.
determined from the maximum speed desired


37.
An oscillator is subjected to a damping force that is proportional to its velocity. A sinusoidal force is applied to it. After a long time:
A.
its amplitude is an increasing function of time
B.
its amplitude is a decreasing function of time
C.
its amplitude is constant
D.
its amplitude is a decreasing function of time only if the damping constant is large
E.
its amplitude increases over some portions of a cycle and decreases over other portions


38.
If the angular velocity vector of a spinning body points out of the page then, when viewed from above the page, the body is spinning:
A.
clockwise about an axis that is perpendicular to the page
B.
counterclockwise about an axis that is perpendicular to the page
C.
about an axis that is parallel to the page
D.
about an axis that is changing orientation
E.
about an axis that is getting longer


39.
The angular velocity vector of a spinning body points out of the page. If the angular acceleration vector points into the page then:
A.
the body is slowing down
B.
the body is speeding up
C.
the body is starting to turn in the opposite direction
D.
the axis of rotation is changing orientation
E.
none of the above


40.
For a wheel spinning on an axis through its center, the ratio of the tangential acceleration of a point on the rim to the tangential acceleration of a point halfway between the center and the rim is:
A.
1
B.
2
C.
1/2
D.
4
E.
1/4


41.
For a wheel spinning on an axis through its center, the ratio of the radial acceleration of a point on the rim to the radial acceleration of a point halfway between the center and the rim is:
A.
1
B.
2
C.
1/2
D.
4
E.
1/4


42.
For a wheel spinning with constant angular acceleration on an axis through its center, the ratio of the speed of a point on the rim to the speed of a point halfway between the center and the rim is:
A.
1
B.
2
C.
1/2
D.
4
E.
1/4


43.
The rotational inertia of a wheel about its axle does not depend upon its:
A.
diameter
B.
mass
C.
distribution of mass
D.
speed of rotation
E.
material composition


44.
Two wheels are identical but wheel B is spinning with twice the angular speed of wheel A. The ratio of the magnitude of the radial acceleration of a point on the rim of B to the magnitude of the radial acceleration of a point on the rim of A is:
A.
1
B.
2
C.
1/2
D.
4
E.
1/4


45.
The magnitude of the acceleration of a point on a spinning wheel is increased by a factor of 4 if:
A.
the magnitues of the angular velocity and the angular acceleration are each multiplied by a factor of 4
B.
the magnitues of the angular velocity is multuplied by a factor of 4 and the angular acceleration is not changed
C.
the magnitues of the angular velocity and the angular acceleration are each multiplied by a factor of 2
D.
the magnitues of the angular velocity is multiplied by a factor of 2 and the angular acceleration is not changed
E.
the magnitues of the angular velocity is multiplied by a factor of 2 and the magnitudeof the angular acceleration is multiplied by a factor of 4


46.
Three identical balls, with masses of M, 2M, and 3M are fastened to a massless rod of length L as shown. The rotational inertia about the left end of the rod is:
A.
ML2/2
B.
3ML2
C.
3ML2/2
D.
3ML2/4
E.
5ML2/4


47.
Three identical balls are tied by light strings to the same rod and rotate around it, as shown below. Rank the balls according to their rotational inertia, least to greatest.
A.
1, 2, 3
B.
3, 2, 1
C.
3, then 1 and 2 tie
D.
1, 3, 2
E.
All are the same


48.
A force with a given magnitude is to be applied to a wheel. The torque can be maximized by:
A.
applying the force near the axle, radially outward from the axle
B.
applying the force near the rim, radially outward from the axle
C.
applying the force near the axle, parallel to a tangent to the wheel
D.
applying the force at the rim, tangent to the rim
E.
applying the force at the rim, at 45° to the tangent


49.
The coefficient of static friction between a certain cylinder and a horizontal floor is 0.40. If the rotational inertia of the cylinder about its symmetry axis is given by I = (1/2)MR2, then the maximum acceleration the cylinder can have without sliding is:
A.
0.1 g
B.
0.2 g
C.
0.4 g
D.
0.8 g
E.
g


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