Question

An electric fan is turned off, and its angular velocity decreases uniformly from 490 rev/min to 150 rev/min in 4.50 s .find the number of revolutions made by the motor in the 4.50 s interval.

Answer 1

The answer involves finding the total number of revolutions of a decelerating fan by converting angular velocities to rev/s, calculating the angular deceleration, and then using it to calculate the number of revolutions over the given time interval.

Step-by-step explanation:

The student's question involves determining the number of revolutions made by a fan motor as it decelerates uniformly. Specifically, we need to calculate how many revolutions the fan makes as it slows down from 490 revolutions per minute (rev/min) to 150 rev/min over a period of 4.50 seconds.

Firstly, we convert the angular velocities from rev/min to rev/s by dividing by 60. The initial angular velocity (ωi) is therefore 490/60 rev/s, and the final angular velocity (ωf) is 150/60 rev/s.

Next, we calculate the angular deceleration (α) using the formula α = (ωf - ωi) / t, where t is the time interval.

Knowing α, we use the formula for the total number of revolutions during uniform angular deceleration: N = (ωi + ωf) / 2 × t / 60, where N is the number of revolutions.

Substituting the values into the formula gives us the total number of revolutions made by the motor during the 4.50 s interval. This calculation combines concepts of angular motion and kinematics to provide the answer.