Question

4(12 points) A uniform rod of length L and mass M is attached at one end to a frictionless pivot and is free to rotate about the pivot in the vertical plane as in Figure. The rod is released from rest in the horizontal position. (a)What are the initial angular acceleration of the rod and the initial translational acceleration of its right end (as shown in Fig.a)? (b)What is its angular speed when the rod reaches its lowest position (as shown in Fig.b)? (c)What is the tangential speed of the center of mass when the rod reaches its lowest position (as shown in Fig.b)? L/2 X CM Pivot Mg (a) (b)

Answer 1

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M, L A a) 4 mg Torque about TA = Mg / I = ML/ a = 7 - Mg4/2 NL13 Moment of inerhial about A Angular acceleration d=39 2 L Initial hanslational acceleration of right here end B. QR = La: LX L x 3 08-9 6) A Tests? Initial Using energy conservation 1.6; + R Ei = koef + P. Et Mg(5) = { Iw? to Tv wet VEH final .. ng* == ( )w • 3 W=39 6) Tangenhal velocity of centre of mass Vem = rw where ray Vem = / 3 Vem [ 324