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The frequency of rotation of a ceiling fan increases from 3r.p.s to 4r.p.s. in 6.28 seconds. Its average angular acceleration is
(A) 1rads2
(B) 0.1rads2
(C) 10rads2
(D) 100rads2

Answer
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Hint Use the formula of the angular acceleration given below and substitute the calculated value of the difference in the frequency of the rotation and the time taken in it and the simplification of this equation, to find the value of the acceleration from it.

Useful formula
The formula of the angular acceleration is given by
α=Δωt
Where α is the angular acceleration of the rotating ceiling fan, Δω is the difference in the frequency of rotation and t is the time taken.

Complete step by step solution
It is given that the
At first, frequency of the ceiling fan, ωi=3r.p.s.=3×2π=6πs1
Then, frequency of the ceiling fan, ωf=4r.p.s.=4×2π=8πs1
Time taken for the rotation of the ceiling fan, t=6.28s
The difference in the angular acceleration is calculated as Δω=ω1ω2
Substitute the known values in it,
Δω=8π6π
Simplifying the above equation, we get
Δω=2πs1
The difference in the value of the frequency is obtained as 2πs1 .
By using the formula of the angular acceleration,
α=Δωt
Substituting the known values in the above equation,
α=2π6.28
By performing the division in the above equation, we get
α=1rads2
Hence the value of the angular acceleration of the rotating ceiling fan is obtained as 1rads2 .

Thus the option (A) is correct.

Note The ceiling fan rotates in the circular motion, hence the velocity considered is angular velocity and the acceleration is the angular acceleration. The frequency considered in the above solution is the same as that of the angular velocity.