SHM and uniform circular motion(INSTANTANEOUS VELOCITY)

velocity of point P

the velocity of point P at the instant t will be directed along the tangent to the circle at P.

magnitude of velocity of P

Its magnitude will be

vp= xnot omega

velocity of N

We know that the motion of N on the diameter DE is actually due to the motion of the pointer P so the velocity of N is actually the component of the velocity v_p in a direction parallel to diamter DE.

Component of velocity of P

This component is:

vp sin(90- theta) = vp cos theta = xnot omega cos theta

The magnitude of velocity N or its speed is

v = xnot omega cos theta = xnot omega cos omega.t

direction of velocity of N

depends upon the phase angle

velocity is maximum

at the mean position

velocity is minimum at

at the extreme position(x = x _o)

final derivation