A solid cylinder is rolling without slipping. What fraction of its kinetic energy is rotational?
A) 1/3
B) 2/3
C) 1/2
D) 1/4
E) 3/4

Question

Quizplus · Accepted Answer

For a solid cylinder rolling without slipping, the total kinetic energy is the sum of translational and rotational kinetic energy. The rotational kinetic energy is (1/2)Iω², where I = (1/2)MR² for a solid cylinder. The translational kinetic energy is (1/2)Mv². Since v = Rω, the rotational kinetic energy is (1/4)Mv². Therefore, the fraction of kinetic energy that is rotational is (1/4)Mv² / [(1/2)Mv² + (1/4)Mv²] = 1/3.

A Solid Cylinder Is Rolling Without Slipping