An electric motor is running at 1800 rev min⁻¹. It comes to rest in 20 s. If the angular acceleration is uniform find the number of revolutions it made before stopping. (300 revs) 


Given:

Initial angular velocity = Ѡi = 1800 rev/min = `\frac {1800 rev}{60 s}` = 30 rev s⁻¹
Final angular velocity = Ѡf = 0 rev s⁻¹
Time = t = 20 s

To Find:

The number of revolutions (angular displacement) = Δ𝜭 = ?

Solution:

The formula for angular displacement is

Δ𝜭 = Ѡ Δt  ------------(1)

Here the angular velocity Ѡ will be taken as the average angular velocity `\ overline {Ѡ}` and is calculated as

Ѡ  = `\ overline {Ѡ}` = `\frac {Ѡi + Ѡf}{2}`

by putting values

Ѡ   = `\frac {30 rev s⁻¹ + 0 rev s⁻¹}{2}` = 15 rev s⁻¹

Now putting values in equation (1) we have

Δ𝜭 = Ѡ Δt = 15 rev s⁻¹ ｘ 20 s = 300 rev ---Ans.

Thus, the motor has completed 300 revs before stopping. 



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