1.
An
astronaut stands at the back end of a rocket ship traveling with a velocity V
in the x direction. The astronaut
quickly moves toward the front of the spaceship and suddenly stops, then moves
forward again quickly, stopping at the front. Qualitatively describe what happens to the center-of-mass of
the rocket ship/astronaut system during throughout this event. How does the astronautŐs motion affect
that of the rocket ship?

2.
Consider
a right cylindrical can with mass M, height H, and uniform density that is
initially filled with soda pop of mass m. Small holes are punched in the bottom and top of the
can and the liquid slowly drains out.
What is the height h of the center of mass of the can and pop system
initially? What is the center of
mass of the system after all the liquid has drained out (ignore the soda on the
floor). If x is the height of the
remaining soda pop at any given instant, find x (in terms of M, H, and m) when
the center of mass reaches its lowest point.

3.
In
rewind mode, many cassette and video recorders have one spool that turns at
constant angular velocity pulling the tape from the other spool. What happens to the angular velocity of
the other spool as the tape moves from one spool to the other (changing the
outer radii of the spools). Why?

4.
A
wheel (call it wheel A) of radius 10 cm is coupled by a rubber fan belt to a
different wheel (call it B) of radius 25 cm. Wheel A increases its angular speed from rest at a uniform
rate of 1.2 rad/s^{2}.
Find the time for wheel B to reach a rotational speed of 100 rev/min,
assuming the belt does not slip.

5.
An
early method of measuring the speed of light makes use of a rotating slotted
wheel. A beam of light passes
through a slot on the outside edge of the wheel, travels to a distant mirror,
and returns to the wheel just in time to pass through the next slot in the
wheel. One such slotted wheel has
a radius of 5.0 cm and 500 slots at its edge. Measurements taken when the mirror was 500 m from the wheel
indicated a speed of light of 3.0x10^{8} m/s. a) What was the (constant) angular speed of the wheel? b) What was the linear speed of a point
of the edge of the wheel?