Question

A car has wheels each with a radius of 30 cm. It starts from rest and (without slipping) accelerates uniformly to a speed of 15 m/s in a time of 8.0 s. Find the angular acceleration of its wheels and the number of rotations one wheel makes in this time

Answer 1

Step-by-step explanation:

A point on the rim of the wheel went from rest to 15 m/s so we can solve for the acceleration as

`v = v_0 + at \Rightarrow a = (v)/(t) = \frac{15\:\text{m/s}}{8.0\:\text{s}}`

or

`a = 1.9\:\text{m/s}^2`

We also know that the angular acceleration
`\alpha` is

`a = r\alpha \Rightarrow \alpha = (a)/(r)`

Using r = 0.30 cm and a = 1.9 m/s^2, we get

`\alpha = (a)/(r) = \frac{1.9\:\text{m/s}^2}{0.30\:\text{m}}`

`\;\;\;\;=6.3\:\text{rad/s}^2`