Calculate the rotational inertia of a meter stick

Question

Mass of the meterstick is 0.749 kg, about an axis perpendicular to the stick and located at the 42.1 cm mark

Calculate the rotational inertia of the meterstick

Answer 1

This is easily solved using the parallel axis theorem which is

I_{moment of inertia through any axis} = I_{axis through center of mass} + mass x d² where d is the distance from center of mass to the new axis. the moment of inertial for rotation through the center of mass of a meter stick is

1/12 x mass x L² where L is one meter.

I_{axis through new axis} = 1/12 x 0.749kg x 1²m² + 0.749kg x (0.5 m - 0.421 m)²m² = 0.0671 kg m²