Question

A cylinder of radius 3.09cm and a spherical shell of radius 7.22cm are rolling without slipping along the same floor. The two objects have the same mass. If they are to have the same total KE, what should the ratio of the cylinders angular speed to the spherical shell's speed be?

Answer 1

Here,

let the angular speed of cylinder is wi and spherical shell is w2

Now, for the same Kinetic energy

0.50 * I1 * w1^2 = 0.50 * I2 * w2^2

0.50 * m * 3.09^2 * w1^2 = 2/3 * m * 7.22^2 * w2^2

0.50* 3.09^2 * w1^2 = 2/3 * 7.22^2 * w2^2

Now, for w1/w2

w1/w2 = 2.69

the ratio of the cylinders angular speed to the spherical shell's speed be 2.69