As the hydraulic cylinder rotates around O, the exposed length l of the piston rod is controlled by the action of the oil pressure in the cylinder. If the cylinder rotates at the constant rate of dθ/dt = 55 deg/s and l is decreasing at the constant rate of 155 mm/s, calculate the magnitudes of the velocity v and acceleration a of end B when l = 125 mm.

At the instant shown, the paper is being unrolled with a speed, vp = 7.5m/s and an acceleration ap = 1 m/s2. If, at this instant, the outer radius of the roll is r= 0.75 m, determine the angular velocity ωs and acceleration αs of the roll

At the instant shown, the disk is rotating with an angular velocity of wo = 3 rad in the clockwise direction. Determine the x-component of the velocity vector of pin A (in m) at this instant. Consider r = 1.0 meters and 0 = 35°. A 2r B. a y

The T shaped plate is rotating at a rate of w = 10 rad/s CCW (as shown) and deccelerating at a rate of a = -2.5 rad/s². The relevant dimensions of the plate are a = 3 in and b = 2 in. The plate is inclined at an angle = 15 deg at the instant shown. 1. What are the inertial velocity and acceleration vectors of points P and Q in terms of the unit vectors 6₁ and 6₂? 2. Which point has a greater velocity magnitude? acceleration magnitude? 3. How much of the acceleration is due to the Coriolis effect? 4. How many revolutions will the plate complete before reaching zero angular velocity? iz a b₂ 9 ......... b Q a