Question

After fixing a flat tire on a bicycle you give the wheel a spin. If its initial angular speed was 6.36 rad/s and it rotated 14.7 revolutions before coming to rest, what was its average angular acceleration (assuming that the angular acceleration is constant)

Answer 1

To solve this problem we will apply the concepts related to the cinematic equations of angular motion. On these equations, angular acceleration is defined as the squared difference of angular velocity over twice the radial displacement. This is mathematically:

$\alpha = \frac{\omega^2-\omega_0^2}{2\theta}$

Our values are,

$\text{Initial angular velocity} = \omega_0 =6.36 rad/s$

$\text{Final angular velocity} = \omega =0$

$\text{Angular displacement} = \theta = 14.7rev = 29.4\pi rad$

Replacing,

$\alpha = \frac{- 6.36^2}{29.4\pi}$

$\alpha = -0.43rad/s^2$

Therefore the angular acceleration is $-0.43rad/s^2$