Question

A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a vertical axle through the center of the disk. The platform has a radius of 1.80 m and a rotational inertia of 347 kg·m² about the axis of rotation. A 58.4 kg student walks slowly from the rim of the platform toward the center. If the angular speed of the system is 1.49 rad/s when the student starts at the rim, what is the angular speed when she is 1.02 m from the center?

Answer 1

R = radius of disk = 1.80 m

I = rotational inertia = 347 kgm²

W_i = initial angular velocity = 1.49 rad/s

r = final distance of student from center = 1.02 m

I_i = initial total moment of inertia = I_disk + I_student = (0.5) MR² + mR² = 347 + (58.4) (1.80)²

I_f = Final total moment of inertia = I_disk + I_student = (0.5) MR² + mr² = 347 + (58.4) (1.02)²

using conservation of angular momentum

I_i W_i = I_f W_f

(347 + (58.4) (1.80)² ) (1.49) = (347 + (58.4) (1.02)²) W_f

W_f = 1.96 rad/s