The cable attached to the sectorshaped rigid body has a cons

The cable attached to the sector-shaped rigid body has a constant speed of 4 m/s, as shown, and there is no slip between the sector and the cable. At the instant shown, the link BD is perpendicular to OA. a) Determine the angular velocity of the links BD and AD, as well as the sector-shaped rigid body b) Determine the angular acceleration of the links BD and AD c) Determine the acceleration of point D, and express it as a vector, choosing suitable unit vector directions

Solution

Angular velocity of link OA = 4/ 0.2 = 20 rad/s

Velocity of point A = W(OA) x OA = 20 x 0.125 = 2.5m/s

Angular velocity of link AD = Va / AC = 2.5/2 = 12.5 rad/s

Velocity of point D = W(AD) x CD = 12.5x0.15 = 1.875 m/s

Angular velocity of link BD = Vd/ BD = 1.875/0.25 = 7.5 rad/s