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 4.67 m and a rotational inertia of 342 kg·m² about the axis of rotation. A 70.8 kg student walks slowly from the rim of the platform toward the center. If the angular speed of the system is 2.28 rad/s when the student starts at the rim, what is the angular speed when she is 1.82 m from the center?

I would appreciate if you guys could show me step by step and also show formulas , I am a little confuse with the physics notation in this chapter , thank you

Answer 1

By, the principle of conservation of angular momentum, total momentum before the student started walking in and after he reached 1.82 m from the center must be equal

For a region with moment of inertia I and angular velocity , angular momentum is given by

Initial momentum when the student started walking is

m is the mass of the student and r and the radisu of the disc

Now the student is at a distance r1 from the cneter. Hence, angular momentum is

Applying the onservation law

This is the new angular speed aafter the student has moved to the new location.