# How to calculate torque required to rotate assembly about the center

The image is a hollow cylinder: 2in OD, 1.76in ID. Connected is an angled bracket, 45 deg, that weighs 3lbs. The top rectangle piece connected to the bracket is 10 lbs,the dimensions are 31.1in x 14.1in x 1.97in . The bottom of the cylinder has a bracket where the motor will attach to. I am planning on using a continuous rotation servo motor. I am trying to figure out how to calculate the torque required to rotate the assembly about the center, vertical axis of the cylinder and am not sure where to start. The biggest part I am stumped on is getting the moment of inertia of the assembly due to the awkward shape of it. Even just a general idea of how to calculate it/procedure will be greatly appreciated.

• If you've used a CAD program to generate the image you should be able to get it to calculate the moment of inertia. Just make sure that you've specified the materials and thicknesses correctly and chosen the correct axis of rotation. Remember that you need to calculate your acceleration torque, not the running torque which will be less. Oh, and go metric, man, it's so much cleaner. Jan 30, 2021 at 21:50
• since this looks like solidworks, if you go to mass properties, you will get a window with all the inertia properties. See youtube link for an example. Jan 30, 2021 at 22:26

• You need to be concerned with other factors that impact the system as soon is it passes the transient time it accelerates from $$\omega=0 \to \omega_{final}$$

Those are friction, air drag, vibration, etc.

Going back to your question, We are going to ignore the contribution of the cylinder both because of its mass and it's being almost at the center of rotation. the general formula for mass moment of inertia for a solid about an inclined axis at one of its ends is:

Let's name the variables

• m = mass of the plate

• a = effective length of the plate= 31.1in* 0.707

• b= 14.1in

The thickness is figured in the mass.

$$I_z=\frac{1}{12}m(4a^2+b^2)$$

if we know the acceleration of the part we need we can figure out the torque:

$$\tau=I_z* \alpha$$