
The frequency of rotation of a ceiling fan increases from to in seconds. Its average angular acceleration is
(A)
(B)
(C)
(D)
Answer
148.8k+ views
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
Where is the angular acceleration of the rotating ceiling fan, is the difference in the frequency of rotation and is the time taken.
Complete step by step solution
It is given that the
At first, frequency of the ceiling fan,
Then, frequency of the ceiling fan,
Time taken for the rotation of the ceiling fan,
The difference in the angular acceleration is calculated as
Substitute the known values in it,
Simplifying the above equation, we get
The difference in the value of the frequency is obtained as .
By using the formula of the angular acceleration,
Substituting the known values in the above equation,
By performing the division in the above equation, we get
Hence the value of the angular acceleration of the rotating ceiling fan is obtained as .
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.
Useful formula
The formula of the angular acceleration is given by
Where
Complete step by step solution
It is given that the
At first, frequency of the ceiling fan,
Then, frequency of the ceiling fan,
Time taken for the rotation of the ceiling fan,
The difference in the angular acceleration is calculated as
Substitute the known values in it,
Simplifying the above equation, we get
The difference in the value of the frequency is obtained as
By using the formula of the angular acceleration,
Substituting the known values in the above equation,
By performing the division in the above equation, we get
Hence the value of the angular acceleration of the rotating ceiling fan is obtained as
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.
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