Question

A bicycle wheel of diameter 80cm accelerates uniformly from rest to angular speed of

50rad/s in 20s.

(a) Find the angular acceleration of a wheel.

(b) If a small stone is stack between the grooves of a wheel, find its tangential and radial

acceleration.

(c) During this time, how many revolutions has this wheel turned?

(d) If the wheel turns through 250rev in coming to rest, at what rate was the angular velocity

changing?

Answer 1

(a) $\omega=\epsilon t\to\epsilon=\omega/t=50/20=2.5\ (rad/s^2)$

(b) $a_{\tau}=\epsilon r=2.5\cdot0.4=1\ (m/s^2)$

$a_n=\omega^2r=50^2\cdot0.4=1000\ (m/s^2)$

(c) $n=\frac{\phi}{2\pi}=\frac{\epsilon t^2}{2}\cdot\frac{1}{2\pi}=\frac{2.5\cdot 20^2}{2}\cdot\frac{1}{2\cdot 3.14\pi}\approx79.6\ (rev)$

(d) $\phi=\frac{\omega^2}{2\epsilon}\to250\cdot2\pi=\frac{\omega^2}{2\epsilon}\to$

$\epsilon=\frac{\omega^2}{2\cdot250\cdot2\pi}=\frac{50^2}{2\cdot250\cdot2\cdot3.14}=0.796\ (rad/s^2)$ .