Question

A bicycle has wheels of 0.70 m diameter. The bicyclist accelerates from rest with constant acceleration to 22 km/h in 10.8 s. What is the angular acceleration of the wheels?

Answer 1

Answer:

$\alpha=0.16\frac{rad}{s^2}$

Explanation:

Angular acceleration is defined as the variation of angular speed with respect to time:

$\alpha=\frac{\omega}{t}$

The relation between the angular speed and the linear speed is given by:

$\omega=\frac{v}{r}$

Replacing (2) in (1):

$\alpha=\frac{v}{rt}$

We need to convert $\frac{km}{h}$ to $\frac{m}{s}$:

$22\frac{km}{h}*\frac{1h}{3600s}*\frac{1000m}{1km}=6.11\frac{m}{s}$

Recall that:

$r=\frac{d}{2}=\frac{0.7m}{2}=3.5m$

Replacing:

$\alpha=\frac{6.11\frac{m}{s}}{(3,5m)(10.8s)}\\\alpha=0.16\frac{rad}{s^2}$