Question

Find the kinetic energy of the sphere if the moment of inertia is given by 2/5MR^2.

Answer 1

KE rot = (1/2)Iw^2 where the moment of inertia I is 2/5MR^2. M is the mass in kg, R is the radius in meters, and w is angular speed in rads/sec.

KE rot = (1/2)(2/5•MR^2)(w^2)

KE rot = (1/5)MR^2•w^2 — in Joules.

Since w = v/R, where v is linear speed…

KE rot = (1/5)Mv^2 in joules