Question

A 0.025m radius toy top is spinning at a rate of 150rpm, what is the angular velocity? What is the linear velocity of the paint on the outside edge?

Answer 1

A) The angular velocity of the disk is 150 rpm (revolutions per minute). We can convert it into proper units, i.e. radiants per seconds, keeping in mind that:
$1 rev = 2 \pi rad$
$1 min = 60 s$
so the angular speed is
$\omega = 150 \frac{rev}{min} = 150 \frac{2 \pi rad}{60 s} =15.7 rad /s$

b) The linear velocity is given by
$v=\omega r$
since the radius is r=0.025 m, the linear velocity at the edge of the disk is
$v= \omega r = (15.7 rad/s)(0.025 m)=0.39 m/s$