Question

A pulley is turning at 30 revolutions per second slows down uniformly to 20 revolutions per second in 2 seconds .

Calculate the number of revolutions it make to a complete stop.

Answer 1

$\omega=\omega_0-\epsilon t \to \epsilon=(\omega_0-\omega)/t=(2\pi\nu_0-2\pi\nu)/t=$

$=(2\cdot3.14\cdot30-2\cdot3.14\cdot20)/2=31.4\ (rad/s^2)$

$\phi=\omega_0^2/(2\epsilon)=(2\cdot3.14\cdot30)^2/(2\cdot31.4)=565.2\ (rad)$

$N=\phi/(2\pi)=565.2/(2\cdot3.14)=90\ (rev)$. Answer