**EXAMPLE 1: MOTION RELATIVE TO MOVING FRAME**

Calculate
the velocity and acceleration of the particle P that is moving with constant
speed _{}relative to the disc along the groove. The bar OA is rotating
with a constant counter-clockwise rotation of _{} relative to the
ground and the disc D is rotating at a constant CCW rate of _{} relative to OA. The
length of OA is *l*.

**SOLUTION:**

## To calculate the velocity we have

_{}

## Note that

_{}

_{}

_{}

_{}

_{}

Substitution
into (1) to get the velocity of P, this gives

_{}

To
get the acceleration we have

_{}

Note
that

_{}

_{}

_{}

_{}

_{}

Substitution
into (2) gives the acceleration of P as

_{}