Question

A solid sphere is given a kinetic energy E. What
fraction of kinetic energy is associated with
rotation?
a) 3/7
b) 5/7
c) 1/2
d) 2/7​

Answer 1

Answer:

If the sphere is rolling at velocity v, the kinetic energy is

KE = 0.5*m*v² + 0.5*I*ω²

I (moment of inertia of the sphere) = (2/5)*m*r²

ω = v/r

KE = 0.5*m*v² + 0.5*(2/5)*mr²*(v/r)²

KE = 0.5*m*v² + (1/5)*m*v²

Total KE = (7/10)*m*v²

The fraction that is rotational is (1/5) / (7/10) = 2/7 or 0.286

(d) is correct option