# Angular acceleration of a flywheel

#### WMDhamnekar

A flywheel is brought from rest up to a speed of 1500 rpm in 1 minute. What is the average angular acceleration, α?

There are four choices available to select.

3)2.617 radians per second per second.

4)5.23 radians per second per second.

5) doubtful

I know the formulas for computing final angular position and final angular velocity. Suppose $\theta_0$= initial angular position, $\theta$= final angular postion,$\omega_0$=initial angular velocity,$\omega$=final angular velocity,$\alpha$= angular acceleration, t=time. then $1)\theta=\theta_0+\omega_0*t+\frac12\alpha*t^2$,

$2)\omega=\omega_0+\alpha*t$,

$3)\omega=\theta_0+\frac12(\omega_0+\omega)*t$,

$4)\theta=\theta_0+\omega*t-\frac12\alpha*t^2$

How to use one of these formula here? I know by changing the position of $\alpha$ we can compute it. I tried for it, but i didn't get any of the answer provided by the author.

Last edited:

#### romsek

MHF Helper
They want average angular acceleration.

$a = \dfrac{\dot{\theta}_f - \dot{\theta}_i}{\Delta t} = \dfrac{\frac{1500}{60}2\pi - 0}{60} = \dfrac{50\pi}{60} = \dfrac 5 6 \pi ~rad/s^2 \approx 2.617 ~rad/s^2$

• WMDhamnekar

#### WMDhamnekar

They want average angular acceleration.

$a = \dfrac{\dot{\theta}_f - \dot{\theta}_i}{\Delta t} = \dfrac{\frac{1500}{60}2\pi - 0}{60} = \dfrac{50\pi}{60} = \dfrac 5 6 \pi ~rad/s^2 \approx 2.617 ~rad/s^2$
Hello,

What is rpm? Is it rounds per minute or radians per minute?

#### romsek

MHF Helper
rpm is revolutions per minute

1 revolution is 2 pi radians

• WMDhamnekar