**EXAMPLE 4: ****KINEMATICS OF RIGID BODIES**

Calculate
the velocity and acceleration of point *D*
if at the current instant the cart has a constant velocity of _{} and the rectangular
plate C has an angular velocity _{} and angular
acceleration _{}.

SOLUTION:

Velocity
of *D*:

_{}

Point
*O* moves with the cart_{}

_{}

The
length of *OD* is constant. Therefore,

_{}

_{}

_{}

Substitution
into (1) gives

_{}

Acceleration
of *D*:

_{}

The
cart has constant velocity so that its acceleration is

_{}

Using
(3) we get

_{}

_{}

_{}

Substitution
yields,

_{}

_{}

Substitution
into (4) yields

_{}