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

Step-by-step 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`

Step-by-step 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* 4.1)\\\\a=(3.14-6.28)/(4.0)\\\\a=-0.79rad/s^2`

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