# How to calculate the required torque in a static equilibrium system

I am working on a personal project where I need to select a motor to rotate a system that is in static equilibrium. The motor torque specification is given in kg.cm.

This is what I have: Bar : 2 meters in length, weighing 1kg (for simplicity) Axle: 10mm (5mm radius) with a bearing to reduce friction. F : F1 and F2 both weigh 10kg

  (F1)       (F2)
10kg       10kg
-------o-------
^
T1               -T2


I am not entirely sure what all the parameters are to arrive at a formula to use. Also, what formula can I use to calculate the torque required to rotate the system at a constant speed of 3rpm ?

I would disregard friction and drag.

let's say an estimated acceleration to get to 3rpm is 10 seconds.

$$I=(1/12ml^2)_{bar}+(2*10*1^2)_{10kgmass}=\\1/12*1*4+20=1/3kg+20kg=20.33kg.m$$

This line added after OP's comment

Using Newton's second law $$F*dt= \Delta mv\quad or\ \tau dt=\Delta L=\omega I$$

$$\tau dt=I\omega=20.33*3/60=61/60\ \approx 1 kgm^2/s$$

plugging 10s for dt we get the torque.

$$10\tau= 1, \ \tau=1/10*9.8 \approx 1Nm,\ or\\ \tau= 10kg.cm$$

Now by changing dt to up or down you get the torque you need.

• Thank you very much for the detailed answer. If you don't mind, briefly explain to me how you went about the calculation. I did look at Inertia, but by that time I was already very confused. – Tino Fourie Dec 7 '20 at 1:41
• @TinoFourie, we use Newton's 2nd law but in rotational acceleration. T=Ialpha as F=ma. then we multiply both sides by dt to get alphadt= angular velocity and Tdt = alphadtI= rotation velocityI= omega*I. we calculated the I and we plug angular acceleration. later I will add steps to my answer to clarify this. – kamran Dec 7 '20 at 3:16
• I thank you for your time, patience, and explanation. – Tino Fourie Dec 8 '20 at 11:08

If:

• 3rpm is the constant velocity that your system will rotate
• you are not worried about how fast you accelerate to 3rpm
If you wanted to get within an order of magnitude(or two), I would suggest assuming an angular acceleration $$\alpha$$ which would get you from zero to the constant velocity in a reasonable for your project time, and then multiply that by the moment of area ($$I= \frac{1}{12}m_{bar}L_{bar}^2$$).