Question

A disc is rotating with angular velocity w, a force f acts at a point whose position vector with respect to the axis of rotation is vector r. The power associated with torque due to the force is given by

Answer 1

Power is
$p = force \times veocity$
here torque is replaced as force.
Here torque is
$f \times r \sin( \alpha )$
where alpha is angle between force and radius vector.
as both are perpendicular,so,
$torque = f \times r$
as given angular velocity 'w',so linear velocity is
$v = rw$
now put power formula and you will find,
$power = torque \times veocity \\ so \: power = f \times r \times rw \\ power = f {r}^{2} w$
there is a figure for better understanding
thanks.
Tripathy.