Question

Two 2 kg masses is placed at either end of a rod that has a mass of .5 kg and a length of 3 m. What is the moment of inertia if the system it is rotated about (a) one end of the rod and (b) the center of the rod?

Answer 1

Explanation:

a) $I=\displaystyle \sum_{i}m_ir_i^2$

where $r_i$ is the distance of the mass $m_i$ from the axis of rotation. When the axis of rotation is placed at the end of the rod, the moment of inertia is due only to one mass. Therefore,

$I= mr^2 = (2\:kg)(3\:m)^2 = 18\:kg-m^2$

b) When the axis of rotation is placed on the center of the rod, the moment is due to both masses and the radius r is 1.5 m. Therefore,

$\displaystyle I= \sum_{i}m_ir_i^2 = 2(2\:kg)(1.5\:m)^2 = 9\:kg-m^2$