Question

The initial angular velocity of a ceiling fan is 6.28 rad/s. It accelerates uniformly to 3.14 rad/s in 4.0 s. What is the angular acceleration?

Answer 1

Answer: 18.84 rad/s

Explanation:

V = u + at

V = 6.28 + (3.14 x 4 )

V = 18.84 rad/s

Answer 2

Answer: The angular acceleration of the fan is $-0.79rad/s^2$

Explanation:

To calculate the angular acceleration of the fan, we use first equation of motion:

$v=u+at$

where,

v = final angular velocity of the fan = 3.14 rad/s

u = initial angular velocity of the fan = 6.28 rad/s

a = angular acceleration of the fan = ?

t = time = 4.0 sec

Putting values in above equation, we get:

$3.14=6.28+(a\times 4.1)\\\\a=\frac{3.14-6.28}{4.0}\\\\a=-0.79rad/s^2$

Hence, the angular acceleration of the fan is $-0.79rad/s^2$