Problem Q1: The small cylinder is made to move along the rotating rod with a motion r = r0 +b sin( 2 ! t/ " ), where t is the time counted from the instant the cylinder passes the postion r = r0 and is the period of the oscillation (time for one complete oscillation). Simultaneously, the rod rotates about the vertical at the constant angular rate d ! /dt. Determine the value of r for which the radial ( r-direction acceleration is zero. Problem Q3: In the differential pulley hoist shown, the two upper pulleys are fastened together to form and integral unit. The cable is wrapped around the smaller pulley with its end secured to the pulley so that it cannot slip. Determine the upward acceleration a B of cylinder B if cylinder A has a downward acceleration of 2 ft/s 2 . (Suggestion: Analyze geometrically the consequences of a differential movement of cylinder A ). Ans. a B = 0.25 ft/s 2 (up) Problem Q4: Three gears 1, 2, and 3 of equal radii are mounted on the rotating arm as shown. (Gear teeth are omitted from the drawing.) Arm OA rotates clockwise about
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Physical quantities, constant angular rate, upward acceleration aB