Answer:
[tex]\alpha = 52.1[/tex]
Explanation:
Given
[tex]w_1 = 250\ rad/s[/tex] --- initial angular velocity
[tex]t_2 = 4.8s[/tex] -- Initial time
Because the engine completely stops, we have the following:
[tex]w_2 = 0\ rad/s[/tex] --- final angular velocity
[tex]t_1 = 0[/tex] --- final time
Required:
Determine the angular acceleration ([tex]\alpha[/tex])
The angular is calculated as thus:
[tex]\alpha = \frac{w_2 - w_1}{t_2 - t_1}[/tex]
i.e. the ratio of change in angular velocity to change in time
Substitute in the required values, the expression becomes:
[tex]\alpha = \frac{250 - 0}{4.8 - 0}[/tex]
[tex]\alpha = \frac{250}{4.8}[/tex]
[tex]\alpha = 52.08333[/tex]
[tex]\alpha = 52.1[/tex] -- approximated
Hence, the engine's angular acceleration is 52.1rad/s^2
