Question

A fan blade rotates with angular velocity given by ωz(t)= γ − β t2, where γ = 4.90 rad/s and β = 0.750 rad/s3 . part a calculate the angular acceleration as a function of time.

Answer 1

Angular acceleration, α = -2βt

Step-by-step explanation:

Angular velocity of fan is
`\omega_(z(t))=\gamma -\beta t^2`

`\gamma=4.90\ rad/s`

`\beta=0.750\ rad/s^3`

Angular acceleration is given by :

`\alpha=(d\omega)/(dt)`

`\alpha=(d(\gamma -\beta t^2))/(dt)`

`\alpha=-2\beta t`

Hence, the above equation is the angular acceleration as a function of time.

Answer 2

The angular velocity as a function of time is given by

`\omega (t)=\gamma-\beta t^2`
where
`\gamma=4.90 rad/s` and
`\beta=0.750 rad/s^3`. The angular acceleration as a function of time is equal to the derivative of the angular velocity. If we calculate the derivative of w(t), we find:

`\alpha(t)= (d\omega)/(dt) =-2\beta t`
and this is the angular acceleration of the fan blade.