A 1.2-lb block B slides without friction inside a slot cut in arm OA which rotates in a vertical plane at a constant rate, theta = 2 rad/s. At the instant when theta = 30 degrees, r = 2 ft and the force exerted on the block by the arm is zero. Determine, at this instant, (a) the relative velocity of the block with respect to the arm, (b) the relative acceleration of the block with respect to the arm.
a) Along the theta direction:
F = m*(dw/dt + 2*vr*w)
where, w = angular velocity of the arm = 2 rad/s
Because no force is acting on the block, this force will be balanced by a component of gravity ...
We solve (a) by first finding the component of gravity perpendicular to the arm. We solve (b) by finding the relative acceleration of the block with respect to arm in radial direction.