A small block B rests on a horizontal plate which rotates ab

A small block B rests on a horizontal plate which rotates about a fixed axis. The plate starts from rest at t = 0 and is accelerated at the constant rate of 0.5 rad/s^2. Knowing that r = 200 mm, determine the magnitude of the total acceleration of the block when (a) t = 0, (b) t = 1 s, (c) t = 2 s. The belt sander shown is initially at rest. If the driving drum A has constant angular acceleration of 120 rad/s^2 counterclockwise, determine the elation of the belt at point C and at the work station D, two seconds after sander has been turned on.

Solution

Angular acceleration = 120 rad / s^2

Acceleration of belt = radius * angular acceleartion

= 2.25 * 120

= 270 in / s^2

Velocity after 2 sec = u + at = 0+ 270*2 = 540 in/ sec

centripital acceleration at c= v^2 / r = 540^2 / 2.25 = 129600 in/ s^2

Total acceleration at C = Underroot of ( 129600^2 + 270^2) = 129600.28 in/ s^2

Acceleration at D = 270 in / s^2