Problem 22
What is a rigid body? How many degrees of freedom does it have?

Problem 23
Motion of a heavy symmetric top.

Problem 17
What are the properties of the symmetric matrix?

Problem 22
What is the general definition of principal axes of inertia?

Problem 23
What is happening when 3 principal axis of inertia are equal?

Problem 24
What is center of instantaneous rotation?

Problem 25
Discuss a nontrivial example that involves an axis of instantaneous rotation

Problem 18
How do you derive the inertia moment w/r of an axis n when given the inertia tensor?

Problem 19
Show where the parallel axis theorem helps to solve the problem

Problem 20
State the Euler theorem and show what is a rotation.

Problem 21
Write the angular velocity in rotating reference frame

Problem 22
Derive the Euler equation

Problem 24
Discuss the motion of a free symmetric top

Find the torque that is needed to rotate a rectangular plate with a constant angular velocity directed along the diagonal of the plate.

Problem 24
Find the potential and kinetic energy of the cylinder rolling down the inclined plane. Discuss the diference between hollow and solid cylinder.

Problem 25
A cube with edge 2a and mass M glides with constant velocity on a frictionless table. At the edge of a table it bumps against an obstacle and tilts over the edge. Find the minimum velocity v0 such that cube still falls from the table.

Problem 26
Given a homogeneous cone spinning on its vertex find the precession frequency.

Problem 25
Discuss the stability of the rotations of a rigid body with tensor of inertia I and
Iz > Iy > Ix

Problem 26
Find the components of angular velocity for a free rotating top.

Problem 27
Prove that nutation angle is constant for a free rotating top

Problem 28
Find three constants of motion for a heavy symmetric top. Define them in terms of Euler angles.

Problem 22 What is a rigid body? How many degrees of freedom does...