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

`\alpha=0.16(rad)/(s^2)`

Step-by-step explanation:

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

`\alpha=(\omega)/(t)`

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

`\omega=(v)/(r)`

Replacing (2) in (1):

`\alpha=(v)/(rt)`

We need to convert
`(km)/(h)` to
`(m)/(s)`:

`22(km)/(h)*(1h)/(3600s)*(1000m)/(1km)=6.11(m)/(s)`

Recall that:

`r=(d)/(2)=(0.7m)/(2)=3.5m`

Replacing:

`\alpha=(6.11(m)/(s))/((3,5m)(10.8s))\\\alpha=0.16(rad)/(s^2)`