Question

A car starts from rest and its wheels constantly accelerate to an angular velocity of 2 rad/s after two revolutions. What is the angular acceleration of the wheel?

Answer 1

`alpha=1/(2pi) "rad s"^(_2)`

Explanation:

with angular constant acceleration problems, you can use the constant angular acceleration equations, which are similar to the more familiar constant acceleration eqns.

so if `omega_i="initial angular velocity"`

`omega_f="final angular velocity"`

`alpha="angular acceleration"`

`theta="angular displacement"`

we have

`omega_f^2=omega_0^2 +2 alpha theta`

in this question
`omega_i=0" " rad" " s^(-1)`

`omega_f=2 " "rad" " s^(-1)`

`alpha="angular acceleration"`

`theta= 4pi" " rads`

`2^2=0 +2 alpha xx4pi`

`8alphapi=4`

`alpha=4/(8pi)=1/(2pi) "rad s"^(_2)`