This review packet was compiled by Professor Cummings (cummik2@rpi.edu).
It is a compilation of appropiate review questions for the spring '98 exam#2.
These questions came from old exams #2, old exams #3 and the finals.
Work hard and good luck.
PART A.
QUIZ 2             2 NOVEMBER 1994

___ 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

B. near the surface of the earth

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

___ 6. Figures 1 and 2 below show a meter stick, half of which is wood and half of which is steel. (Steel is denser than wood.) In figure 1, the stick is pivoted at the wooden end, at O, and a force F is applied to the steel end. In figure 2, the stick is pivoted at the steel end, at O', and an identical force is applied to the wooden end. A. The angular acceleration will be greater for the stick in figure 1, because the torque about O is   greater than the torque about O'.

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.

QUIZ 2            27 MARCH 1995

____ 4. The law of conservation of momentum applies to a system of colliding objects only if:

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:

A. the greater speed                      D. the greater momentum

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

C. the smaller momentum

___ 6. Three identical objects of mass M are fastened to a massless rod of length L as shown. The rotational inertia about one end of the rod of this array is:

A) ML2/2
B) ML2
C) 3ML2/2
D) 5ML2/4
E) 3ML2

QUIZ 2            25 MARCH 1996 ___ 3. A uniform narrow bar, resting on ice, is given a transverse horizontal impulse J at one end as shown. The center of mass of the bar, CM, will then:                        A. remain at rest                 D. move in a parabola

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

C. move in a straight line

___ 4. A cart, loaded with sand, rolls along a horizontal frictionless track. As the cart moves, sand trickles out at a constant rate through a hole in the bottom of the cart. The speed of the cart will:                    A. decrease at a constant rate               D. decrease at a variable rate

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

C. remain the same

___ 5. The surface of the earth moves from west to east due to the earth's daily rotation. Therefore, the angular velocity vector of the earth, due to its daily rotation, is directed:                    A. tangent to the equator toward the east     D. due south

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

C. due north

___ 6. The figure shows a cylinder of radius 0.7 m rotating about its axis at 10 rad/s. The speed of the point P is:

A) 7.0 m/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

___ 6. A solid cylinder made of lead has the same mass and the same length as a solid cylinder made of wood. The density of lead is greater than the density of wood. The rotational inertia of the lead cylinder compared to the wooden one is: A. greater                       D. need to know the radii

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

C. same

QUIZ 3                   12 DECEMBER 1994

___ 1. When a woman on a frictionless rotating turntable extends her arms out horizontally, her angular velocity: 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

___ 2. When a woman on a frictionless rotating turntable extends her arms out horizontally, her kinetic energy: A. must increase

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

___ 1. Two uniform, solid cylinders have different masses and different rotational inertias. They simultaneously start from rest at the top of an inclined plane and roll without slipping 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. A man, holding a weight in each hand, stands at the center of a horizontal frictionless rotating turntable. The effect of the weights is to double the rotational inertia of the system. As he is rotating, the man opens his hands and drops the two weights. They fall outside the turntable. Then: A. his angular velocity doubles

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

QUIZ 3 1 MAY 1996

___ 1. 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: A. moves to the left and rotates counterclockwise

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:

A. tangent to the equator toward the east               D. due south

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

C. due north

QUIZ 3 30 APRIL 1997

___ 1. A student is standing on a frictionless turntable that is free to rotate about a vertical axis through the student's center of mass (just as in the class activity). The student and turntable are initially at rest. A second student throws a heavy ball at a speed v, which the student on the turntable catches. When the ball is caught, it is a distance R from the axis of rotation, as shown in the sketch.

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

FINAL EXAMINATION DECEMBER 16, 1994

___ 10. 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

___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:

A. tangent to the equator toward the east

B. tangent to the equator toward the west

C. due north

D. due south

E. toward the sun

___12. 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

___14. A rod rests on frictionless ice. While forces that are equal in magnitude and opposite in direction are simultaneously applied to its ends as shown, the quantity that remains zero is its:
A. angular momentum
B. angular acceleration
C. total linear momentum
D. kinetic energy E. rotational inertia

___15. 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

FINAL EXAMINATION MAY 8, 1995

_____10. A rifle of mass M is initially at rest but free to recoil. It fires a bullet of mass m and velocity v (relative to the ground). After firing, the velocity of the rifle (relative to the ground) is:

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

___12. 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

__ 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:

A. moves to the left and rotates counterclockwise

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

PART B.

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.

QUIZ 3 1 MAY 1996

1. (6%) A figure skater is spinning about a vertical axis with her arms outstretched. The ice on which she is skating can be considered frictionless for this problem. If she pulls her arms in close to her body:

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

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

QUIZ 3 30 APRIL 1997

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.)

2. (12 pts) A body of mass 4.0 kg is traveling in the positive x-direction and is subjected to a force, also in the x-direction, that varies with time as shown in the graph.

a) (6 pts) The force gives an impulse of 72.0 N-s to the body in the time interval between t = 0 and t = 5.0 s. What is the value of F at t = 2.0 s (i.e its maximum value)?
F = _________ ____
units
b) (6 pts) If the body was moving at 8.0 m/s at t = 0, what is its speed at t = 5.0 s? The force shown in the graph is the net force acting on the body.

FINAL EXAMINATION DECEMBER 16, 1994.

1. (12 pts) The diagram below represents two identical particles sliding on a horizontal frictionless surface, before and after they collide. Their masses are m1 = m2 = 0.35 kg. Before the collision, m2 is at rest and m1's speed is v1i = 10.0 m/s. After the collision, m1's speed is v1f = 8.0 m/s and m2's is v2f = 6.0 m/s.
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, draw an arrow on the diagram showing the direction.

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

b) (6 pts) Do you have enough information to determine whether the collision was elastic? 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?

PART C.
QUIZ 2 2 NOVEMBER 1994

1. (46%) The diagram shows a cart with four (4) wheels that is moving on a level surface with a constant speed of v = 2.0 m/s. The wheels roll without slipping, and have an angular velocity of w = 8.0 rad/s. The mass of the entire cart (including the wheels) is 30 kg, and its total kinetic energy is 92.0 J.

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

d) (8%) Find the rotational inertia of one of the wheels.

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: _________________

QUIZ 2 27 MARCH 1995

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.

a) (10%) At the bottom of its swing, just before it collides with the rod, the speed of the ball is v0 = 6.0 m/s. What is the value of h, the height from which the ball was released?

h = _________ ____
units
The ball collides with the rod, rebounds, and starts the rod rotating, as shown in the sketch below. Immediately after the collision, before the ball and rod have moved as far as shown in the sketch, the ball's velocity is v = - 2.0 m/s and the kinetic energy of the rod is Krod = 24.0 J..

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 _______________
d) (10%) Find the magnitude of the angular velocity of the rod immediately after the collision, when it had a kinetic energy of 24.0 J. [Hint: For a uniform thin rod, I about the center of mass is, Icm = ML²/12, and I about an end is Iend = ML²/3.]

w = _________ ____
units
e) (6%) Find the maximum value of q, the angle between the rod and the vertical direction. That is the angle at which the rod's kinetic energy becomes zero, and the rod momentarily comes to a halt.

q = _________ ____
units

QUIZ 2 25 MARCH 1996

1. (46%) Car B is stopped at a traffic signal on a slippery road, as shown in the sketch. Car A, unable to stop on the slippery road, crashes into the rear of the car B. The cars lock together and skid forward as one for 20.0 meters before they stop. Their speed immediately after the collision is 9.0 m/s. The mass of car A is mA = 1500 kg, and the mass of car B is mB = 1000 kg.

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

v = _________ ____
units
b) (9%) Was the collision elastic? (i.e. was it a perfectly elastic collision?) Circle the correct answer and show appropriate numerical evidence to support your answer. (Do not simply say, "It is obvious.")

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?

J = _________ ____
units
d) (9%) Find the magnitude of the work done by friction as the two cars skidded to a halt.

W = _________ ____
units
e) (9%) What was the magnitude of the average frictional force that the road exerted on the cars as they skidded to a halt?

F = _________ ____
units

QUIZ 2 26 MARCH 1997. 1. (46 pts) The diagram below represents two identical particles sliding on a horizontal frictionless surface, before and after they collide. Their masses are m1 = m2 = 0.35 kg. Before the collision, m2 is at rest and m1's speed is v1i = 11 m/s. After the collision, m1's speed is v1f = 7.0 m/s and m2's is v2f = 5.0 m/s. The angle between the direction of m1's velocity before and after the collision is 20° as shown in the diagram.

a) (10%) Find q, the angle between the direction of v2f, m2's velocity after the collision, and the direction of v1i, m1's velocity before the collision. Express the answer in degrees.

q = ___________

b) (6%) Find the magnitude of the impulse given to m2 during the collision.

J2 = _________ ____
units
c) (6%) Find the magnitude of the impulse given to m1 during the collision.

J1 = _________ ____
units

d) (6%) Find the magnitude of the velocity of the center of mass of the two particles.

vcm = _________ ____
units

e) (10%) Was kinetic energy of translation conserved during the collision between m1 and m2? (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.

KRotation = _________ ____
units

FINAL EXAMINATION MAY 8, 1995

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

a) (6 pts) While the blocks are accelerating, which, if either, is greater, T1 or T2? Circle the correct answer. T1 IS GREATER; T2 IS GREATER; T1 = T2.

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

R = _________ ____
units
c) (9 pts) Find the kinetic energy of the entire system (consisting of both blocks and the pulley) after the hanging block has fallen 0.50 m.

K = _________ ____
units
d) (9 pts) Is there friction between the plane and the sliding block? Circle the correct answer and justify your answer by an appropriate numerical calculation.
THERE IS FRICTION; THERE IS NO FRICTION