Question

A pendulum in the form of a thin square plate (1 mx 1 m) is released from rest at the position shown, with its center of mass at a 45° angle from vertical. The pendulum has a mass of m = 2 kg, and a Moment of Inertia about its center of gravity G of 16 mba, where b is the width of the plate. Find: (a) The moment of inertia about point A (using the parallel axis theorem). (b) The initial angular acceleration a of the plate. 0 G 0 = 45° O b = 1 m m = 2 kg b = 1 m

Answer 1

D liven; dimensions of plate- mx Jo=45 G balm Mars of plate - 2kg = Mo I about Go Its t mb² 2kg balm centre use a) MOI about Az We know MOI of square plate about it's of gravity ie G. In order to find parallel anis theorem. According In Tot (m)Cedas)" ] law it's MOI about A, we to which dan feb 24 SIMS Imbt me IAF (2)(1) + $(2)() + m g 3 + 2 2 2 In = $+1 4 3 egenz TA

angular ular acceleration of 45 G mg b) initial square plate 2 2 2 The plate will notate about if left free initially Torque on plate will act about a due to If it's initial angular ular acceleration IAR (mg) (6/2) az (mg 6/2) (2) (9.8) (12) IA then rad 3² 4/3 & 7.35 rad s²