PHYSICS 206
Problem set 6

Given March 11 1999
Due March 19 1999


Problem 1:
A thin uniform plank of length l mass M lies at rest on a friction-less surface. The plank is given a horizontal kick (momentum transfer P) at one end normal to the plank. Describe the subsequent motion in terms of translational and angular velocity

a:

about the center of mass.

b:

about the point kicked.

c:

Is there a point on the plank where the initial velocity after the kick is zero?

Problem 2:
(Fowler and Cassiday 9.4)
A uniform block of mass m and dimensions a by 2a by 3a spins about a body diagonal with angular velocity $\omega$.

a:

Find the kinetic energy.

b:

Find the angle between the angular momentum and the angular velocity.

Problem 3:
A sphere of radius a has a spherical cavity of radius a/2 centered at a distance a/2 from the center of the center of the sphere. Except for the cavity the mass is uniformly distributed.

a:

Find the center of mass of the object. Find the moments of inertia with respect to the center of the sphere.

b:

Find the moments of inertia with respect to the center of mass.

Use coordinate systems in which the z-axis goes through the centers of the sphere and the cavity.

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