Amotor running at 2600 rev/min is suddenly switched off and decelerates uniformly to rest after 10 s. find the angular deceleration and the number of rotations to come to rest?

Angular acceleration = (change in angular speed) / (time for the change)

change in angular speed = (zero - 2,600 RPM)  =  -2,600 RPM

time for the change = 10 sec

Angular acceleration = -2600 RPM / 10 sec = -260 rev / min-sec

(-260 rev/min-sec) x (1 min / 60 sec) = -(4 1/3)  rev / sec²

Since the acceleration is negative, the motor is slowing down.
You might call that a 'deceleration' of (4 1/3) rev/sec² .

The average speed is  1/2(2,600 + 0) = 1,300 rev/min = (21 2/3) rev/sec.

Number of revs = (average speed) x (time) = (21 2/3) x (10sec) = (216 2/3) revs

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