3- D Kinematics

Let P be any point on the body and d its distance from the axis. Then P has the speed . Let r be the position vector of P referred to coordinate system with origin O on the axis of rotation. Then

, where is the angle between and r. Therefore,

is the tangential speed. There is no normal component of speed.

Thus the velocity V of point P is

Note that velocity of point P is normal to both and r.

The acceleration can be found by differentiating the above equation. Thus,

...........................(i)

since