PHY 372 HW #51. Find the moment of inertia for a square

PHY 372 HW #51. Find the moment of inertia for a square pyramid of uniform density (square base 4 other sides meeting at a point at the top). Each side of the square base has length a. The height of the pyramid is 1.5a. Put the base in the x-y plane and put the origin in the center of the square. Thus the z-axis goes through the point at the top. Find the moment of inertia tensor for this object.2. A triangular lamina of mass m is drawn below. For the coordinate system in the drawing find (a) the moment of inertia tensor; (b) the moment of inertia about the diagonal 45( between the positive x and y axes (and passing through the origin); (c) the angular momentum about the origin if the lamina is spinning with angular rate w about this diagonal; (d) the kinetic energy of part c; (e) a set of principal axes3. A rigid body consists of 8 particles each of mass m. The particles are located at the vertices of a rectangular box. The box itself has no mass. Put the origin of this object is at the center of the box and make the box undergo free rotation at ( about an axis that is in the y-z plane and makes an angle of 20( with the z-axis as shown in the figure below.Find (a) period of precession of the axis of rotation about the symmetry axis (b) the period of wobble of the symmetry axis about the invariable line and (c) the angle between ( and L.4. C9.1y3aaxxyz4aaa
Attachments: