A machine part has the shape of a solid uniform sphere of mass 225 g and diameter 3.00 cm. It is spinning about a frictionless axle through its center, but at one point on its equator it is scraping against metal, resulting in a friction force of 0.0200 N at that point. (a) Find its angular acceleration. (b) How long will it take to decrease its rotational speed by 22.5 rad/s?

Solution 11E Step 1: a) Torque on the sphere, = I Where, I - Moment of inertia - Angular acceleration Or, we can write, torque, = force × radius of the sphere = F r Provided, radius of the sphere, r = D/2 = 3 cm / 2 = 1.5 cm = 0.015 m Frictional force acting on the sphere, F = - 0.0200 N Moment of inertia of a solid sphere, I = MR 2 Therefore, we can write, Fr = MR 2 Mass of the sphere, M = 225 g = 0.225 kg Therefore, - 0.0200 N × 0.015 m = × 0.225 kg × (0.015 m) × 2 Rearranging , = (- 0.0200 N × 0.015 m) / ( × 0.225 kg × (0.015 m) ) 2 2 = (- 0.0200 N × 0.015 m× 5 ) / (2 × 0.225 kg × (0.015 m) ) 2 Angular acceleration, = - 14.81 rad/s