17-119 - 17119 The 30-kg uniform slender rod AB rests in the position shown when the couple moment of M = 150 N m is applied Determine the initial

# 17-119 - 17119 The 30-kg uniform slender rod AB rests in...

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M 150 N m 0.75 m A B 0.75 m 17–119.The 30-kguniform slender rod ABrestsin the positionshown when the couple moment of iapplied. Determine the initial angular acceleration of therod. Ne s g lect the ma ss of the roller s . M = 150 N # m SOLUTION Equations of Motion: Here, the ma ss moment of inertia of the rod about it s ma ss center i s . Writin g the moment equation s of motion about the inter s ection point A of the line s of action of and and u s in g , Fi g . a , ; (1) Kinematics: Applyin g the relati v e acceleration equation to point s A and G , Fi g . b , Equatin g the i component s , (2) S ub s titutin g Eq. (2) into Eq. (1), Ans. a = 6.667 rad > s 2 = 6.67 rad > s 2 ( a G ) x = - 0.75 a ( a G ) x i + ( a G ) y j = - 0.75 a i - a A j ( a G ) x i + ( a G ) y j = - a A j + ( - a k ) * ( - 0.75 j ) - a G = a A + a * r G > A - v 2 r G > A 5.625 a - 22.5( a G ) x = 150 - 150 = 30( a G ) x (0.75) - 5.625 a + © M A = © ( M k ) A N B N A I G = 1 12 ml 2 = 1 12 (30)(1.5 2 ) = 5.625 k g # m 2