A solid sphere, with a mass of 3 kg, is rolling across a horizontal floor without slipping. The sphere has 8.4 J of total kinetic energy and has a center of mass velocity of 2 m/s. Calculate the rotational kinetic energy of the solid sphere.

2.4 J

Explanation:

The total kinetic energy of the solid sphere = rotational kinetic energy + translational kinetic energy

KE(total) = KE(rot) + KE(trans)

KE(rot) = KE(total) - KE(trans)

Since its total kinetic energy KE' = 8.4 J and its mass, m = 3 kg and the velocity of its center of mass, v = 2m/s, KE(trans) = 1/2mv² = 1/2 × 3 kg × (2 m/s)² = 3 kg × 2 m²/s² = 6 kgm²/s² = 6 J

So, KE(rot) = KE(total) - KE(trans)

Substituting the values of the variables, we have

KE(rot) = 8.4 J - 6 J

KE(rot) = 2.4 J

So, the rotational kinetic energy of the solid sphere is 2.4 J

cant without the picture! ?