The disk with circular slot of 200 mm radius rotates about O

The disk with circular slot of 200 mm radius rotates about O with a constant angular velocity omega = 15 rad/s. Find the acceleration of the slider A at the instant when it passes the centre of the disk if, at that instant, theta = 12 rad/s and theta = 0.

Solution

Coriolis Acceleration = 2* (Omega x v)

v = velovity at the instant = 12 * 0.2 = 2.4 m/s

Therefore, Coriolis acceleration = 2 * 15 * 2.4 Sin 90 = 72 m/s² along y axis ( k x i = j)

Acceleration due to motion the circular slot = Omega² x r = 12²x0.2 = 28.8 m/s² along -j

Therefore, total acceleration = 72 - 28.8 = 43.2 m/s²along y-axis = 43.2 j m/s²