Relative to the Earthfixed coordinate system the disk rotate

Relative to the Earth-fixed coordinate system, the disk rotates about the fixed point O with a constant angular velocity of 10 rad/s. Determine the velocity and acceleration of point A relative to point B at the instant shown.

Solution

velocity of point A wrt to centre of disk, vA = w r (-i)

vA = - 20 ft/s i

Velocity of B, vB = (10 x 2 ) (j) = 20 ft/s j

velocity of A wrt to B, vAB = vA - vB = - 20 i - (20 j) = - 20i - 20 j ft/s ........Ans

magnitude of acceleration of point at distance r, a = w^2 r

and direction is alway towards the centre of disc.

aA = (10^2 x 2) (-j) = - 200 ft/s^2 j

aB = (10^2 x 2 )(-i) = - 200 ft/s^2 i

aAB = aA - aB

= - 200 j - (-200i) = - 200 j + 200 i ft/s^2

aAB = 200i - 200 j ft/s^2