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

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.