# A machinist turns the power on to a grinding wheel, at rest, at time t=0 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 29 rad/s. The wheel slows down...

A machinist turns the power on to a grinding wheel, at rest, at time t=0 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 29 rad/s. The wheel slows down uniformly at 2.7 rad/s^2 until the wheel stops/ In this situation , the average angular velocity in the time interval form t=0 s to t=25 s closest to :

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You need to evaluate the average angular velocity, under the given conditions, such that:

`alpha = (omega_f - omega_i)/(t - t_0)`

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

The problem provides the acceleration `alpha = 2.7 (rad)/s^2` and interval of time, hence, you may evaluate the average velocity, such that:

`Delta omega = Delta t*alpha`

`Delta omega = (0 - 25)*(-2.7)`

The minus sign means that the wheel slows down, hence, deccelerates, such that:

`Delta omega = 25*2.7`

`Delta omega = 67.5 (rad)/s`

**Hence, evaluating the average velocity, under the given conditions, yields `Delta omega = 67.5 (rad)/s` .**