A fan initially rotating at 60 rad/sec clockwise accelerates and acquires an angular velocity of 110 rad/sec clockwise. If the angular acceleration of the fan is constant and it takes 2 sec to change its angular velocity, find the angular acceleration.

The correct option is (C)

The equation of rotational motion for constant angular acceleration is given by

ω_f = ω_i  + αt

⇒ α = \(\frac{\omega_f - \omega_i}{t}\)

Where, 

• ω_f = final angular velocity
• ω_i = initial angular velocity
• α = angular acceleration
• t = time taken to reach final angular velocity from initial angular velocity.

Taking the clockwise direction as -ve and counterclockwise as +ve.

Given, 

Initial angular velocity of the fan, ω_i = – 60 rad/s

final angular velocity of the fan, ω_f = – 110 rad/s

Time taken, t = 2 sec

Using the equation of rotational motion, angular acceleration (α) of the fan, is given by 

α = \(\frac{(-110)-(-60)}{2}\) = – \(\frac{50}{2}\)

⇒ α = – 25 rad/sec²

Negative sign shows that the angular acceleration of the fan is in the clockwise direction.

Hence, the angular acceleration of the fan is 25 rad/sec² in clockwise direction.

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