# Torque Required for Rotating a Cylinder

1. Apr 24, 2015

### Alvaro Vargas

Hello everyone, I am new to this forum, and here is my first question.

I need some help in a particular case regarding torques. Most of the examples given anywhere on the web and books have rotations which are affected directly by gravity like pulleys and such, but, what if I want to calculate the torque needed for a servomotor that's under a cylinder with a certain mass and radius which makes it to rotate at constant RPM about its axis, not horizontally, but vertically, kind of like a plinth.

Would (T.of.motor)= (mass.of.cylinder* gravity * radius.of.cylinder) in a practical way?

2. Apr 24, 2015

### Staff: Mentor

Welcome to the PF.

By "plinth", I take it that the cylinder is vertical, and you want it to rotate about its vertical axis?

In any case, the torque required to keep it rotating at a constant angular velocity is zero, except for the torque required to overcome losses like friction. The torque that is required to spin it up to speed is the same torque to overcome the losses, plus τ = I * α. Where I is the Moment of Inertia, and α is the angular acceleration. Are you familiar with Moments of Inertia? http://en.wikipedia.org/wiki/Moment_of_inertia

3. Apr 24, 2015

### Alvaro Vargas

Exactly, the cylinder is vertical and I want it to rotate about its axis.

I am somewhat familiar, I=(m*r^2)/2 for a solid cylinder, but that's where my dilemma comes in, a servomotor has a pre established maximum torque, the one that I'm using is about 5.1 kg-cm, so if I have that maximum torque and the moment of inertia from the cylinder, does it mean the cylinder will just rotate with an angular acceleration= t/I?

It doesn't make too much sense to me, that would mean any cylinder could rotate regardless of the moment of inertia, just with very low angular accelerations if I is too large.

4. Apr 24, 2015

### Staff: Mentor

That sounds like a pretty small motor. How big/heavy is the cylinder?

If there is no friction or other losses, then a small motor can spin up a heavy cylinder, just pretty slowly. But for real systems, you will have bearing friction, which is usually maximum when the cylinder is not moving (similar to how the static coefficient of friction is generally larger than the dynamic one). And it will be the stall torque of the motor that will have to overcome that bearing friction. Is gearing down the motor an option?

5. Apr 24, 2015

### Alvaro Vargas

The weight of the cylinder is about 30 Kg and has a 12 cm radius, I'am also neglecting friction since the drum is over a bushing, maybe that could be interchanged with a safety percentage (I don't know what percentage would be adequate for it), so, if I'm not wrong, and I hope you could redirect me, by the amount of weight I assume I would have to gear down the motor, probably to about a 3:1 ratio to ensure movement. So if I gear it down, the torque would be 5*3 Kg-cm and its maximum rated speed would be 54 RPM/3, and after it I would have to recalculate angular acceleration which would mean a little increase on how fast it starts to move?

That seems more like I'm finding how fast it is going to start moving, not if the motor is strong enough to start moving the drum, am I wrong?

6. Apr 24, 2015

### Staff: Mentor

Do you have a motor in mind? Can you post a link to its datasheet? What is its rated stall torque?

Do you have the cylinder and bearings already? You can measure the torque it takes to overcome its static friction, and compare that to the motor's datasheet numbers...

7. Apr 24, 2015

### Alvaro Vargas

The datasheet is this one, it doesn't say much besides what I have described before though:

https://www.pololu.com/product/1248/specs

And I'm not using bearings, just a base that makes barely any contact with the bottom part of the drum and it will be well lubricated.