A sphere of radius 1.59 cm and a cylinder of radius 7.47 cm are rolling without

Question

A sphere of radius 1.59 cm and a cylinder of radius 7.47 cm are rolling without slipping along the same floor. The two objects have the same mass. If they are to have the same total kinetic energy, what should the ratio of the sphere's angular speed to the cylinder's angular speed be?

A sphere of radius 1.59 cm and a cylinder of radius 7.47 cm are rolling without slipping along the same floor. The two objects have the same mass. If they are to have the same total kinetic energy, what should the ratio of the sphere's angular speed to the cylinder's angular speed be?

Explanation / Answer

KEsph=KEcyl

1/2 IsWs^2 = 1/2 Ic Wc^2

Ws/Wc = sqrt(Ic/Is)

= sqrt((1/2 MRc^2)/(2/5 M Rs^2))

= sqrt(5/4)*Rc/Rs

= 5.25265

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