___ 3. The center of mass of the earth's atmosphere is:

A. a little less than halfway between the earth's surface and the outer boundary of the atmosphere

C. near the outer boundary of the atmosphere

D. near the center of the earth

E. none of the above

___ 4. Two identical carts travel at 1 m/s in opposite directions on a common surface. They collide head-on and are reported to rebound, each with a speed of 2 m/s. Then:

A. momentum was not conserved, therefore the report must be false

B. if potential energy were released during the collision, the report could be true

C. if the collision were elastic, the report could be true

D. if the surface were inclined, the report could be true

E. if the duration of the collision were short enough, the report could be true

___ 5. The fan shown has been turned on and is speeding up as it rotates clockwise. The direction of the acceleration of the point X on the fan tip could be:

A. æ B. å C. ã D. ä E. â

B. The angular acceleration will be greater for the stick in figure 2, because the torque about O' is greater than the torque about O.

C. The angular acceleration will be greater for the stick in figure 1 because the rotational inertia about O is smaller than the rotational inertia about O'.

D. The angular acceleration will be greater for the stick in figure 2 because the rotational inertia about O' is smaller than the rotational inertia about O.

E. The angular acceleration will be the same in both cases.

A. there is no change in kinetic energy of the system

B. the relative speed of separation is the same as the relative speed of approach

C. the objects stick together

D. the net external force is zero

E. the collisions are all elastic

___ 5. Two bodies of unequal mass, placed on a frictionless surface, are acted on by equal horizontal forces for equal times. Just after these forces are removed, the body of greater mass will have:

B. the greater acceleration E. the same momentum as the other body

C. the smaller momentum

A) ML^{2}/2

B) ML^{2}

C) 3ML^{2}/2

D) 5ML^{2}/4

E) 3ML^{2}

B. move in a circle E. move along some other curve

C. move in a straight line

B. increase at a constant rate E. increase at a variable rate

C. remain the same

B. tangent to the equator toward the west E. toward the sun

C. due north

A) 7.0 m/s

B) 14p rad/s

C) 7p rad/s

D) 0.7 m/s

E) none of these

**QUIZ 2
26 MARCH 1997**

___ 4. An elastic collision is one in which:

A. momentum is not conserved but kinetic energy is conserved

B. total mass is not conserved but momentum is conserved

C. kinetic energy and momentum are both conserved

D. momentum is conserved but kinetic energy is not conserved

E. the total impulse is equal to the change in kinetic energy

B. less E. need to know the masses and the radii

C. same

**QUIZ 3
12 DECEMBER 1994**

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

B. must decrease

C. must remain the same

D. may increase or decrease depending on her initial angular velocity

E. changes into angular momentum

**QUIZ 3 3 MAY 1995**

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)

B. his angular velocity remains about the same

C. his angular velocity is halved

D. the direction of his angular momentum changes

E. his rotational kinetic energy increases

B. moves to the right and rotates counterclockwise

C. moves to the left and rotates clockwise

D. moves to the right and rotates clockwise

E. moves to the right and does not rotate

___ 2. The surface of the earth moves from west to east due to the earth's
daily rotation. Therefore, the *angular momentum* vector of the earth,
due to its daily rotation, is directed:

B. tangent to the equator toward the west E. toward the sun

C. due north

**QUIZ 3 30 APRIL 1997**

After the ball is caught, the angular momentum vector of the student on the turntable points:

A. to the right D. out of the page

B. to the left E. I missed that class

C. into the page

___ 2. An astronaut finishes some work on the outside of her satellite, which is in circular orbit around Earth. She leaves her wrench outside the satellite. The wrench will:

A. fall directly down to Earth D. fly off tangentially into space

B. continue in orbit with the satellite E. spiral down to Earth

C. continue in orbit at reduced speed

___ 10. An elastic collision is one in which:

B. total mass is not conserved but momentum is conserved

C. kinetic energy and momentum are both conserved

D. momentum is conserved but kinetic energy is not conserved

E. the total impulse is equal to the change in kinetic energy

___11. The surface of the earth moves from west to east due to the earth's daily rotation. Therefore, the angular momentum vector of the earth, due to its daily rotation, is directed:

B. tangent to the equator toward the west

C. due north

D. due south

E. toward the sun

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

A. angular momentum

B. angular acceleration

C. total linear momentum

D. kinetic energy E. rotational inertia

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

**FINAL EXAMINATION MAY 8, 1995**

A. -mv B. -Mv/m C. -mv/M D. -v E. mv/M

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

__ 13. A yo-yo, arranged as shown, is able to roll without slipping on the horizontal surface shown. When a force F is applied to the string, the yo-yo:

B. moves to the right and rotates counterclockwise

C. moves to the left and rotates clockwise

D. moves to the right and rotates clockwise

E. moves to the right and does not rotate

**QUIZ 2 25 MARCH 1996**

2. (6%) The sketch represents a racquet, similar to the one considered
in your spreadsheet problem. The strings are not shown in order to simplify
the picture. The racket is suspended from a peg at point P, and it is free
to swing in a vertical plane about the peg. It comes to equilibrium in
the position shown. On the diagram, mark the position of the center of
mass of the racket with an "*x*". Briefly describe why you chose that
point.

b) (3%) Her angular velocity about the vertical axis will: **INCREASE**;
**DECREASE**; **REMAIN CONSTANT**. (Circle the correct expression;
no explanation required. )

1. (9%) A device used in a classroom activity consists of a metal rod
pivoted at the center, and free to rotate without friction in a horizontal
plane, as shown in the sketch. There are two sliding pieces on the rod,
as shown in the sketch. The rod is started spinning with the sliding pieces
at the ends of the rod. The pieces are pulled inward by applying a force
**F**, as shown, on strings that run parallel to the rod and down through
the axle.

a) (3%) As the sliding pieces move inward, the angular momentum of the system consisting of the rod plus the sliding pieces:

**INCREASES**; **DECREASES**; **REMAINS THE SAME**

(Circle the correct choice. No work need be shown.)

b) (3%) As the sliding pieces move inward, the angular velocity of the system consisting of the rod plus the sliding pieces:

**INCREASES**; **DECREASES**; **REMAINS THE SAME**

(Circle the correct choice. No work need be shown.)

c) (3%) As the sliding pieces move inward, the kinetic energy of the system consisting of the rod plus the sliding pieces:

**INCREASES**; **DECREASES**; **REMAINS THE SAME**

(Circle the correct choice. No work need be shown.)

F = _________
____

units

** **

** **

a) (6pts) Do you have enough information to determine the direction of the velocity of the center of mass of the two particle system after the collision?

YES; NO. Circle the correct choice.

If you circled YES, was it elastic? YES; NO. Circle the correct choice.

If you circled NO, what other information do you need?

a) (7%) What is the radius of one of the wheels?

R = ____________ ____

units

b) (7%) Find the kinetic energy of translation of the cart.

Ktrans = ____________ ____

units

c) (8%) Find the kinetic energy of rotation of one of the four wheels.

Krot = ____________ ____

units

I = ____________ ____

units

e) (8%) The cart collides with a spring of spring constant k = 4600 N/m,
that is attached to a rigid wall, stops, and is pushed back in the opposite
direction. Find the maximum distance that the spring was compressed.

x = ____________ ____

units

f) (8%) After the cart loses contact with the spring, it has the same speed,
2.0 m/s, that it had before it hit the spring, but in the opposite direction.
Find the impulse that the spring delivered to the cart.

J = ____________ ____

units

The direction of J is: _________________

1. (46%) The sketch below shows a uniform thin rod, of length L = 2.0 m and mass M = 9.0 kg, and a massless string with a small ball of mass m = 1.5 kg attached. Both are suspended from the same frictionless pivot. The ball is raised a distance h, as shown, and released from rest.

h = _________ ____

units

b) (10%) Was kinetic energy conserved during the collision? Circle the correct answer, and justify your choice by means of an appropriate numerical calculation.

**KINETIC ENERGY WAS CONSERVED**

** **

**KINETIC ENERGY WAS NOT CONSERVED**

** **

** **

c) (10%) Find the magnitude and direction of the impulse that the ball received from the rod.

J = _________ ____

units

The direction of J was _______________

w = _________ ____

units

q = _________ ____

units

**QUIZ 2 25 MARCH 1996**

a) (10%) What was the speed of car A, just before the collision?

units

**THE COLLISION WAS ELASTIC THE COLLISION WAS NOT ELASTIC**

c) (9%) What was the magnitude of the impulse received by car B during the collision?

units

units

** **

a) (10%) Find *q*, the angle between
the direction of **v**2f, *m*2's
velocity after the collision, and the direction of **v**1i,
*m*1's velocity before the collision. Express
the answer in degrees.

units

c) (6%) Find the magnitude of the impulse given to

units

units

e) (10%) Was kinetic energy of translation conserved during the collision
between *m*1 and *m*2?
(Ignore rotation in answering this part of the question.) Circle the correct
answer and show appropriate numerical evidence to support your answer.

**KINETIC ENERGY WAS CONSERVED**

** **

**KINETIC ENERGY WAS NOT CONSERVED**

f) (8%) The "particles" that collided, were really disks, just as in
the classroom exercise. Each disk had rotational inertia about its center
of mass of *I* = 5.0 ×10-4 kg·m².
After the collision, both disks were observed to be rotating with an angular
speed of *w* = 14 rad/s. Find the combined
kinetic energy of rotation of the two disks.

units

1. (32 pts) Two identical blocks, each of mass M, are connected by a massless string over a frictionless pulley of radius R and rotational inertia I. The string does not slip on the pulley, and it is not known whether or not there is friction between the plane and the sliding block. This system is released from rest. It is found that after the hanging block has fallen 0.50 m, both blocks have a speed of 2.0 m/s, and the pulley is rotating with an angular speed of 20.0 rad/s.

M = 2.0 kg and I = 0.0090 kg-m2

b) (8 pts) Find the radius of the pulley.

R = _________ ____

units

K = _________ ____

units