A uniform solid sphere with a mass of 0.15 kg rolls without slipping with a tangential velocity of 1.0 m/s. The kinetic energy of rotation of the sphere is
A) 30 mJ.
B) 15 mJ.
C) 60 mJ.
D) 45 mJ.

Question

Quizplus · Accepted Answer

The kinetic energy of rotation of a uniform solid sphere is given by (1/2)Iω^2, where I is the moment of inertia and ω is the angular velocity. The moment of inertia of a uniform solid sphere is (2/5)MR^2, where M is the mass and R is the radius. The angular velocity is equal to the tangential velocity divided by the radius. Substituting these values into the equation for kinetic energy, we get:KE = (1/2)(2/5)MR^2(v/R)^2 = (1/5)Mv^2Plugging in the given values, we get:KE = (1/5)(0.15 kg)(1.0 m/s)^2 = 0.03 J = 30 mJTherefore, the correct answer is A.

A Uniform Solid Sphere with a Mass of 0