Question

A fan blade, initially at rest, rotates with a constant acceleration of 0.029 rad/s2. What is the time interval required for it to reach a 6.58-rad displacement after starting from rest

Answer 1

The time interval is
`t = 21.30 \ s`

Step-by-step explanation:

From the question we are told that

The constant acceleration is
`\alpha = 0.029 \ rad / s^2`

The displacement is
`\theta = 6.58 \ rad`

According to the second equation of motion we have that

`\theta = w_i* t + (1)/(2) * \alpha t^2`

given that the blade started from rest

`w_i` which is the initial angular velocity is 0

So

`\theta = 0 + (1)/(2) * \alpha t^2`

=>
`t = \sqrt{ (2 * \theta )/(\alpha ) }`

substituting values

=>
`t = \sqrt{ (2 * 6.58 )/(0.029 ) }`

=>
`t = 21.30 \ s`