EXAM III, PHYSICS 1306
April 30, 2003, Dr. Charles W. Myles
INSTRUCTIONS: Please read ALL of these before doing anything else!!!
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PLEASE put your name on every sheet of paper you use and write on one side of the paper only!!
PLEASE do not write on the exam sheets, there will not be room!
PLEASE show all work, writing down the essential steps in the solution of a problem. Write the
appropriate formulas first, then put in numbers. Partial credit will be LIBERAL, provided that the
essential work is shown. Organized, logical, easy to follow work will receive more credit than
disorganized work.
The setup (PHYSICS) of a problem will count more heavily than the math of working it out.
PLEASE clearly mark your final answers and write neatly. If I can’t read or find your answer, you
can't expect me to give it the credit it deserves.
You will lose credit if you don’t show the units of an answer or if the units are wrong .
PLEASE FOLLOW THESE SIMPLE DIRECTIONS!! THANK YOU!!
An 8.5’’ x 11’’ piece of paper with anything written on it and a calculator are allowed.
Problem 1 (Conceptual Questions) and IS REQUIRED! Work any 2 of the remaining problems for three
(3) problems total. Problem 1 is worth 34 points. Each other problem is equally weighted and worth 33
points, for a total of 100 points.
1. THIS PROBLEM IS MANDATORY!!! CONCEPTUAL QUESTIONS: Answer
briefly, in complete, grammatically correct English sentences. Supplement answers
with equations, but keep these to a minimum and explain what the symbols mean!!
a. Define: Torque, Moment of Inertia, Rotational KE, Angular Momentum.
b. State Newton’s 2nd Law for Rotational Motion. Explain the meaning of any
symbols! (Note: The answer F = ma will receive ZERO credit!)
c. State the conditions for static equilibrium. Explain the meaning of any symbols!
d. See Figure: The round objects roll without slipping down an inclined plane, each
starting at height H above the horizontal. The box slides without friction down
the plane. All round objects have the same radius R. All objects, including the
box, have the same mass M. The moments of inertia
are: Hoop: I = MR2, Cylinder: I = MR2, Sphere:
I = (2MR2)/5. The four objects are released, one at a
time, from the height H. Which object arrives at the
bottom with the greatest speed? Why ? Which arrives
with the smallest speed? Why? What physical
principle did you use to arrive at these conclusions? (You may write equations,
but explain the meaning of the symbols. I want most of the answer in WORDS!)
2. See Figure. A uniform beam, length L = 20 m & mass m = 2,000 kg, rests with its
ends on vertical supports. A machine, mass M = 12,000 kg, rests on the beam, with
its center a distance x = 15 m from the left end (5 m from the right end!).
a. Compute the torque produced by the weight of the beam about an
axis which passes through the left end of the beam.
b. Compute the torque produced by the weight of the machine about
an axis which passes through the left end of the beam.
c. Write equations which describe the conditions for equilibrium of the
beam. This does not mean to just write the general abstract conditions
for equilibrium! It means to APPLY these conditions to the beam and to write the
equations which result from this application.
d. Find the values of the vertical support forces, F1 and F2, at the ends of the beam.
NOTE: WORK ANY TWO (2) OF PROBLEMS 2., 3., or 4. !!!!!
3. The pulley in the figure has mass M = 25 kg and radius R = 0.4 m. It is a uniform,
solid disk with moment of inertia I = MR2. A massless cord is wrapped around it
and a tension force FT is applied. It starts from rest. After FT is applied for 8 s, the
angular speed is  = 35 rad/s.
a. Compute the pulley’s angular acceleration. What is the linear
(tangential) acceleration of a point on the rim of the pulley?
b. What is the net torque acting on the pulley? What physical principle
did you use to do this calculation?
c. If FT is the only force producing a torque, calculate FT.
NOTE: The answers to parts d and e do not depend on the answers to a, b, & c!
d. After FT is applied for 8 s, what are the pulley’s kinetic energy and
angular momentum?
e. After FT is applied for 8 s, what are the linear velocity and radial (centripetal)
acceleration of a point on the rim of the pulley?
4. A thin HOOP of radius R = 0.5 m & mass M = 6.0 kg starts from rest at the top of an
inclined plane (see figure; it looks like a sphere, but it is a hoop!). It rolls without
slipping down the plane. Initially, the height is H = 8.0 m above the bottom of the
plane. The hoop moment of inertia is I = MR2.
V
H = 8.0 m
V=0
=0
Before
H=0
V=?
=?
After
a. What is the gravitational potential energy of the hoop at its initial position?
b. Use energy methods to calculate the linear speed V of the center of mass and the
angular speed  of the hoop when it reaches the bottom of the plane.
c. What is the translational kinetic energy of the center of mass when it reaches
the bottom of the plane? What is the rotational kinetic energy of the hoop when
it reaches the bottom of the plane? What is the angular momentum about an axis
passing through the center of mass?
d. Suppose that the angular acceleration on the hoop as it moves from its highest
point to its lowest point is 10 rad/s2. What is the linear (tangential) acceleration of
a point on the rim?
e. Using the angular acceleration of part d, calculate the net torque on the hoop
during its motion and the time it takes for the hoop to travel from the top to the
bottom. (Hint: To find the time, you also must use the angular speed  found in
part b).