A solid sphere rolling without slipping on a horizontal surface. If the translational speed of the sphere is 2.00 m/s, what is its total kinetic energy?

The total kinetic energy is 2.8m J. (NOTE: m is mass of the sphere)

Explanation:

The total kinetic energy of a sphere is given by the sum of the rotational kinetic energy and the translational kinetic energy. That is,

The rotational kinetic energy is given by

Where is the moment of inertia

and is the angular velocity

The translational kinetic energy is given by

Where is the mass

and is the translational speed (velocity)

∴

But, the moment of inertia of a sphere is given by

Where is mass

and is radius

∴

Also,

∴

Then,

∴

From the question,

Then,

Hence, the total kinetic energy is 2.8m J. (NOTE: m is mass of the sphere)

its c i just checked it

conduction, convection, radiation