Calculate the angular momentum of a solid uniform sphere with a radius of 0.150 m and a mass of 13.0 kg if it is rotating at 5.70 rad/s about an axis through its center.

The angular momentum of the solid sphere is 0.667 kgm²/s

Explanation:

Given;

radius of the solid sphere, r = 0.15 m

mass of the sphere, m = 13 kg

angular speed of the sphere, ω = 5.70 rad/s

The angular momentum of the solid sphere is given;

L = Iω

Where;

I is the moment of inertia of the solid sphere

ω is the angular speed of the solid sphere

The moment of inertia of solid sphere is given by;

I = ²/₅mr²

I = ²/₅ x (13 x 0.15²)

I = 0.117 kg.m²

The angular momentum of the solid sphere is calculated as;

L = Iω

L = 0.117 x 5.7

L = 0.667 kgm²/s

Therefore, the angular momentum of the solid sphere is 0.667 kgm²/s