Question

A car engine is initially rotating at 250 rad/s. It is then turned off and takes 4.80 s to come to a complete stop. What is the angular acceleration of the engine

Answer 1

`\alpha = 52.1`

Step-by-step explanation:

Given

`w_1 = 250\ rad/s` --- initial angular velocity

`t_2 = 4.8s` -- Initial time

Because the engine completely stops, we have the following:

`w_2 = 0\ rad/s` --- final angular velocity

`t_1 = 0` --- final time

Required:

Determine the angular acceleration (
`\alpha`)

The angular is calculated as thus:

`\alpha = (w_2 - w_1)/(t_2 - t_1)`

i.e. the ratio of change in angular velocity to change in time

Substitute in the required values, the expression becomes:

`\alpha = (250 - 0)/(4.8 - 0)`

`\alpha = (250)/(4.8)`

`\alpha = 52.08333`

`\alpha = 52.1` -- approximated

Hence, the engine's angular acceleration is 52.1rad/s^2