Example 1: A uniform rod of length L and mass m is hinged by
a pin and attached at a ceiling with no friction. Someone has
pushed on the rod, and when it moves through the bottom of
its swing it has an angular speed ω. For that given value, find
an expression for the height that the center of mass will reach.
Pin
Example 2: Shown is a uniform, solid sphere of mass M and
radius R which has a string wrapped around its equator. The
string passes over a pulley of radius r and moment of inertia I
and which has no friction in its bearing. At the end of the string,
below the pulley, is a mass m. The system is released from rest.
Find the speed of the mass m once it has moved down a distance
h.
M,R
I,r
m
Example 3: A uniform solid disk with mass m and radius R is
pivoted about a horizontal axis through its center. A small object
of the same mass is glued to the rim of the disk. If the disk is
released from rest with the small object at the end of a horizontal
radius, find the angular speed when the small object is directly
below the axis.
m
R
m
Axis