Question

1) A cylinder of Mass M and radius R, and initial speed V, starts
rolling up an incline of angle theta relative to horizontal. Assuming
no slipping, how high up does the cylinder get?

2) teeter/totter
a) Peewee has mass m and his big buddy Delilah has mass 2m. If Peewee
sits at one end of a uniform teeter totter of length L and mass M, how
far from the central pivot should Delilah sit (ie on the other end) to
be balanced?

b) Delilah instead chooses to sit at the far end from Peewee. What
vertical acceleration does Peewee experience when they start from a
level teeter/totter from 0 angular velocity at horizontal? Provide an
answer that is a function of the angular displacement (theta) from the
horizontal. What normal force does Peewee experience as a function of
theta?

3) A baseball-crazy astronaut in space catches a fastball. What happens?
Let's treat the astronaut as a rod of length L and mass M and assume
the ball of mass m attaches a distance L/5 from one
end. Compute/describe the resultant motion. Note the moment of inertia
for a solid rod is ML^2/12 for rotation around its center of mass. Hint,
you will have to use the parallel axis theorem for moment of inertia.

Answer 1