NAME _______________________
PH125
Exam 3a
April 16, 2012
1. A figure skater goes into a spin with her limbs outstretched. She then brings her limbs in close
to her body, reducing her rotational inertia from 3 kg∙m2 to 1 kg∙m2. Her initial angular velocity
is 4 rad/s. What is her final rotational kinetic energy?
(a) 24 J (b) 72 J (c) 12 J (d) 4 J (e) 36 J
2. Four round objects - solid sphere, hollow sphere, solid cylinder, hollow cylinder - are rolling up
a hill. If they each have the same speed at the bottom of the hill, which object goes the farthest
up the hill before stopping? (Hint: Which has the greatest energy relative to its mass?)
(a) solid sphere (b) hollow sphere (c) solid cylinder (d) hollow cylinder
3. Suppose an asteroid is discovered that orbits the sun in a circular orbit with radius twice that of
earth. The time for the asteroid to make a complete orbit about the sun is
(a) less than 0.5 yr (b) 0.5 yr (c) 2 yr (d) more than 2 yrs
4. A spherical planet has a radius of 10,000 km. If an object weighs 500 N on the surface of the
planet, what would be the gravitational force on the object if it were in a circular orbit 10,000
km above the planet?
(a) 125 N (b) 250 N (c) 500 N (d) 1000 N (e) zero
5. A satellite is in an elliptical orbit about earth. Where in its orbit is its speed the greatest?
(a) farthest from earth (b) closest to earth (c) same everywhere
6. A pendulum has a period of 1 sec on earth and 2 sec on Planet X. What is the acceleration of
gravity on Planet X (in m/s2)?
(a) 2.45 (b) 4.9 (c) 6.9 (d) 13.9 (e) 19.6
7. A 0.2-kg mass oscillates at the end of a spring on a level frictionless table with period 0.5 sec.
What is the maximum elastic potential energy if the amplitude of oscillation is 0.04 m?
(a) 0.5 J (b) 4 J (c) 0.025 J (d) 1.25 J (e) 0.08 J
8. In a physics lab experiment a string is held at a tension of 8 N by a mass hanging from one end
of the string over a pulley. A vibrator at the other end of the string produces the standing wave
pattern shown in the figure. The length vibrator
of the string from the vibrator to the
pulley is 0.75 m, and the mass density
of the string is 0.005 kg/m. What is the
frequency of the vibration?
m
(a) 20 Hz (b) 40 Hz (c) 60 Hz (d) 80 Hz (e) 100 Hz
9. A mass oscillates at the end of a spring with amplitude A. If you take the mass-spring system to
the moon and let it oscillate with twice the amplitude, then compared to its frequency on earth,
the frequency on the moon is
(a) larger (b) smaller (c) the same
10. A motorist traveling at 35 m/s chases an ambulance traveling at 25 m/s which has a siren blaring
at 800 Hz. What frequency does the motorist hear? Assume the speed of sound to be 340 m/s.
(a) 822 Hz (b) 826 Hz (c) 779 Hz (d) 668 Hz (e) 860 Hz
Part 2. Show your work in the space provided.
1. A block of mass mb hangs from a light rope wrapped around a pulley
with rotational inertia I and radius R which is pivoted to rotate about
its axis. The linear acceleration of the block is a, the angular
acceleration of the pulley is α, and the tension in the rope is T.
I
α
(a) Write down Newton's 2nd law of motion for the pulley in terms of
T, R, I, and α.
R
mb
a
(b) Write down Newton's 2nd law of motion for the block in terms of T, mb, g, and a.
(c) What is the relationship between a and α?
(d) Now combine these equations to obtain expressions for T and a.
2. A large spherical asteroid has a radius of 35 km and a mass of 4.5 x 1017 kg.
(a) A 5-kg rock is released from rest 20 km above the surface of the asteroid. What is the initial
potential energy of the rock? (PE = 0 at infinity.) G = 6.67 x 10-11 N∙m2/kg2
PE = ___________ J
(b) What is the potential energy of the rock when it hits the surface of the asteroid?
PE = ___________ J
(c) What is the speed of the rock just before it lands?
v = ________ m/s
3. (a) Write down the expression for the period of oscillation of a physical pendulum (not a simple
pendulum). Define each term in your expression.
(b) A uniform rod of length 2 m is pivoted to oscillate about a point 0.3 m from one end. Find
the period of oscillation. The rotational inertia about a perpendicular axis through the center
1 mL2 , where L is the length of the rod, and the parallel axis theorem gives
of mass is I cm  12
Ip = Icm + md2.
T = _________ sec
4. A transverse wave on a rope is shown
as a plot of y versus x at two different
times.
(a) Write down an explicit expression
for the transverse displacement of
the wave as a function of x and t;
i.e., y(x,t). Include all known
numerical values in the equation.
(b) What is the wave speed?
v = ________ m/s
(c) What is the vertical velocity of the rope at x = 0.5 m and t = 0.02 s?
vy = ________ m/s
(d) If the mass density of the rope is 0.2 kg/m, what is the power transmitted?
P = ________ W