Question

1. A belt of length 25 m runs on a wheel of radius 30 cm. The wheel coasts uniformly to rest from an initial speed of 2 rev s-1. Calculate the 

i)  number of revolutions the wheel turns before it stops.  

ii) angular acceleration of the wheel 

Answer 1

i. $N=l/(2\pi r)=25/(2\cdot3.14\cdot0.3)\approx13.3$

ii. $\omega^2=\omega_0^2+2\epsilon\theta$

$\theta=2\pi N=l/r$

$\omega=0$ . So, we have $\epsilon=\omega_0^2/(2\theta)=\omega_0^2\cdot r/(2l)=(4\pi)^2\cdot 0.3/(2\cdot25)=0.95\ (rad/s^2)$