Question

A wheel of 4cm rad rotates on stationary axis it uniformly speed from rest in a speed of 900 rev/m in a time of 10secs. Find (a) the constant angular acceleration of the wheel (b) tangential acceleration of a point on its rim

Answer 1

Given:

$n_0=0\:\rm rev/s$

$n=900\:\rm rev/s$

$r=0.04\:\rm m$

$t=10\:\rm s$

(a)

$$\beta=\frac{\omega-\omega_0}{t}=2\pi\frac{n-n_0}{t}$$

$$=2\pi*\frac{900-0}{10}=565\:\rm rad/s^2$$

(b)

$$a_{\tau}=\beta r=565*0.04=22.6\:\rm m/s^2$$