1996M3. Consider a thin uniform rod of mass M and length l, as shown above.
a. Show that the rotational inertia of the rod about an axis through its center and perpendicular to its length is Ml2/12.
The rod is now glued to a thin hoop of mass M and radius R/2 to form a rigid assembly, as shown above. The centers of the rod and the hoop coincide at point P . The assembly is mounted on a horizontal axle through point P and perpendicular to the page.
b. What is the rotational inertia of the rod-hoop assembly about the axle?
Several turns of string are wrapped tightly around the circumference of the hoop. The system is at rest when a cat, also of mass M, grabs the free end of the string and hangs vertically from it without swinging as it unwinds, causing the rod-hoop assembly to rotate. Neglect friction and the mass of the string.
c. Determine the tension T in the string.
d. Determine the angular acceleration a of the rod-hoop assembly.
e. Determine the linear acceleration of the cat.
f. After descending a distance H=5l/3, the cat lets go of the string. At that instant, what is the angular momentum of the cat about point P ?