Question

Conceptual Example 14 provides useful background for this problem.

A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 134 kg·m2. When one person is standing at a distance of 1.41 m from the center, the carousel has an angular velocity of 0.595 rad/s. However, as this person moves inward to a point located 0.648 m from the center, the angular velocity increases to 0.841 rad/s. What is the person's mass?

Answer 1

I = 134 kgn? 8=1.41m والمم، لها 0 . 15 82 = 0.648 m W₂ = 0.841 radls M = ? Applying Conservation of angular Momen I. w; = If we I = I + M8, 2 I= I + M8₂² (I + M82) W, = (I + M ) W₂ Iw, + Mz²w, = I wz + Mezzo → Mrzewz - Mr, 2W, = Iw, - I w₂ M (3² W₂ - 82 w.) = I (w, - wa) M = I (w, w). (62 W, -8,2 W,) - M = (134) (0.59-0.841) ((0.648)² x 0.841 - 1.41² 0.595) (M= 39.73 kg