Question

10) A point mass of 4 kg is placed at x = -5 m, y = 0 m, a point mass of 7 kg is placed at x = 0 m, y = +8 m, a point mass of 5 kg is placed at x = 0 m, y = -2 m. The rotational kinetic energy about the y axis (spinning about the y axis) is 119 Joules, how fast are the masses spinning in rad/s?

Answer 1

Here,

the moment of inertia about the y axis is I

Iy = 4 * 5^2 + 7 * 0^2 + 5 * 0^2

Iy = 100 Kg.m^2

let the angular speed is w

Using rotational kinetic energy = 0.50 Iy * w^2

119 = 0.50 * 100 * w^2

w = 1.54 rad/s

the angular speed is 1.54 rad/s