Question

What is the moment of inertial of a 3kg uniform rod with length 2 meters and radius

20cm, if the axis of rotation is located at (a) one end of the rod, (b) at the center of the

rod and (c) through the center?

Answer 1

See the formulas for the moment of inertia here: https://en.wikipedia.org/wiki/List_of_moments_of_inertia.

Let $L=2m$ be the length of the rod, $m=3kg$ be its mass, and $r = 20cm = 0.2m$ be its radius. Then the moment of inertial will be the following.

a) $I = \dfrac13 mL^2 = \dfrac{3kg\cdot (2m)^2}{3} = 4kg\cdot m^2$

b) $I = \dfrac{1}{12} mL^2 = \dfrac{3kg\cdot (2m)^2}{12} = 1kg\cdot m^2$

c) $I = \dfrac{1}{2} mr^2 = \dfrac{3kg\cdot (0.2m)^2}{2} = 0.06kg\cdot m^2$