Express torque as a function of angular velocity

[Catalyst971]

I am strugglin with this step in my assignment. I am dealing with a centrifuge with a known moment of inertia. I should write the expression for a torque of the motor and express it as a function of angular velocity. Can you help me please?

 

[Charles Link]

Next time, please fill out the Homework template. I will notify the mentors that you need to do this next time, and I think your post will be ok this time.
The equation you need is torque $\vec{\tau}=\frac{d \vec{L}}{dt}=I \, (\frac{d\vec{\omega}}{dt})$, where vector $\vec{L} =I \, \vec{\omega}$ is the angular momentum, and $I$ is the moment of inertia about the axis of rotation. $\\$ Note:$\frac{d \vec{\omega}}{dt}=\frac{\Delta \vec{\omega}}{\Delta t}$. $\\$ Since it is basically a rotation about the z-axis, you can ignore the vectors in these equations and write $\tau_z=I \, (\frac{\Delta \omega_z}{dt})$, so that torque $\tau=I \, (\frac{\Delta \omega}{\Delta t})$, where $\omega=\frac{2 \pi}{T}=(2 \pi)$ x (number of revolutions per second)=angular velocity (in radians per second), where $T$ is the period of one revolution.

 

[haruspex]

write the expression for a torque of the motor and express it as a function of angular velocity.

That does not quite make sense. Torque is related to angular acceleration. Please quote the task exactly as given to you.

 

[Charles Link]

@haruspex Torque is a function of the derivative of the angular velocity w.r.t. time. I think we are working with a beginner here, who might not know what a derivative is. Please see my post 2 above.

 

[haruspex]

@haruspex Torque is a function of the derivative of the angular velocity w.r.t. time. I think we are working with a beginner here, who might not know what a derivative is. Please see my post 2 above.

I would still like to to see the verbatim statement of the assignment.