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

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:
$\alpha(t)= \frac{d\omega}{dt} =-2\beta t$
and this is the angular acceleration of the fan blade.

Answer 2

Answer:

Angular acceleration, α = -2βt

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 :

$\alpha=\dfrac{d\omega}{dt}$

$\alpha=\dfrac{d(\gamma -\beta t^2)}{dt}$

$\alpha=-2\beta t$

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