Question

The motor driving a grindstone is switched off when the latter has a rotational speed of 240 rpm. After 10sec, the speed is 180 rpm. If the angular retardation remains constant, how many additional revolutions does it make before coming to rest?

Answer 1

$f_i= \frac{240}{60}=4 rps \\ f_i= \frac{180}{60}=3 rps \\ w_f=2\pi(3)=6\pi rad/s \\ w_f=w_i+\alpha t \\ 6 \pi=2 \pi+\alpha *10 \implies \alpha=-0.2 \pi rad/s^2 \\ w_f^2=w_i^2+2\alpha \theta \\ 0^2=(6\pi)^2+2(-0.2\pi) \theta \implies \theta =\frac{36\pi^2}{0.4\pi}=90\pi rad\\ N= \frac{90\pi}{2\pi}=45 rev$