Question

The triangular plate is pinned to the 11 lb smooth collar. Determine the initial angular acceleration of the plate when P = 50 lb is applied to the collar. The plate is originally at rest. Note that the mass moment of inertia is proportional to the Area moment of inertia by: Imass = lareapt, where the density p = 490 lb/ft and the thickness of the plate t = 12 inch. ор 1.5 ft 1.5 ft

Answer 1

kinetic diagram FBD Collar | Collar - mc ac mpagy c1° mag kbc1.54 < Plate <Pla mpg S Plate & mp aga {=8 x 1.5=8 x 1,5=1,299 ft given mp= mass of plate= 79.5 me= mass of collar- ll lb p= 50 lb teb

Plate mass calculati 'I mass - I cauaxext met - be it bago X me moto (126) x 400 a mort de 15 mp = 7957 eb

→ At equilibrium - - E Fyzo - E Fc= 0 2.P=mcą tmp qGx .:-50= l qt 74.5796x -- timpa Gy=0 EMA=0 2. IX- mp &tr=0 za (He 5% ) = 29. tax r p Gói a 1.5? = b2 < - GC 8 r 8 X 1.299 Qafq=0.2165 x ---- 2 ภา

Collar - Acceleration of point A is equal to accm of Gc= cla= aatra q=0.2165 2 + 1.299 a - ac=1.5155 2 -_-(3) Pretting this value in eq? (1) 50=11 qct 79, 02 aGx 50 = 5(1.51550)+ 79.5700.21654) "-2.0158 rad/22 - Initial angular - acceleration of Plate

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