VELOCITY AND ACCELERATION EQUATIONS FOR 2 POINTS ON THE SAME RIGID BODY

We have derived equations to determine the velocity and acceleration of a point on an arbitrarily moving body. What happens if we need to determine the velocity and acceleration of 2 points on an arbitrarily moving body?

• Basically, we can consider one point on the body to be out O' origin of B.
• We can then assume that the point P on the body is the other point of interest.

For P on the body B, = 0 and

Consider acceleration:

Again a_P/B = 0 and V_P/B = 0 as the point P is located on the body itself.

One of the concepts that we used in planar theory was the concept of an instantaneous center of velocity. Does it's 3D counterpart - an instantaneous axis of rotation exist ?

- Not always. Example - Motion such as a rolling cylinder on the floor.