Question

The pulley shown (Figure 1) has a moment of inertia IA = 0.625 kg⋅m2 , a radius r = 0.250 m , and a mass of 20.0 kg. A cylinder is attached to a cord that is wrapped around the pulley. Neglecting bearing friction and the cord’s mass, express the pulley’s final angular velocity in terms of the magnitude of the cord’s tension, T (measured in N), 4.00 s after the system is released from rest. Use the principle of angular impulse and momentum.

B

Answer 1

Solution - Given mass of Pulley (m) = 20 20 kg Vadius of Pulley r=0.25 m moment of Innentia IA = 0.625 kg. m2 t₂ = 4 Free Body Diagram . AX Ay Mar.T mg - 0.25 T T At Rest tico W = 0 from Principle of Angular impulse and momentym ta IAW, t S. MA dt - IA Wz 0.625 X o t 0.25 T lidt = 0.625 * Wy

0.62 ХО б. 625 0, (озят) 4] « (ч-о) о: 2г Тх о: 42 0, О-2 xчx T L, - 662 у Со, - 1. 6 Т. Ang