A solid uniform ball with a mass of 125 g is rolling without slipping along the horizontal surface of a table with a speed of 4.5 m/s when it rolls off the edge and falls towards the floor,1.1 m below.What is the rotational kinetic energy of the ball just before it hits the floor?
A)0.51 J
B)0.73 J
C)1.1 J
D)2.6 J
E)This question cannot be answered without knowing the radius of the ball.

Question

Quizplus · Accepted Answer

The rotational kinetic energy of a rolling ball is given by (1/2)Iω², where I is the moment of inertia and ω is the angular velocity. For a solid sphere, I = (2/5)mr² and ω = v/r. Substituting these into the equation gives (1/2)(2/5)mr²(v/r)² = (1/5)mv². Using m = 0.125 kg and v = 4.5 m/s, the rotational kinetic energy is (1/5)(0.125)(4.5)² = 0.51 J. The radius is not needed as it cancels out.

A Solid Uniform Ball with a Mass of 125 G