# How to calculate the torque from a free rotation object?

1. Jan 12, 2012

### keithlaw

Hi everyone,

A question just pop up from my head.

Imagine a rigid body cylinder is rotating freely about its z-axis with a known angular velocity. Let's say the whole system is frictionless. How can I get the value of the torque at the center of the z-axis?

Is the net force on this free rotational body equals zero even though it is rotating?

Why I have a thought of it is because I want to know if the spinning wheel of a car will apply any torque to the drive shaft if the car is coasting.

2. Jan 12, 2012

### rcgldr

If angular velocity of an object is constant, then there is no net torque on that object. There could be equal and opposing torques on that object that cancel out, resuting in a net torque of zero.

3. Jan 12, 2012

### keithlaw

"There could be equal and opposing torques on that object that cancel out, resulting in a net torque of zero."
Could you please rephrase this sentence? If there is no net torque, how can I calculate the equal and opposing torques?

4. Jan 12, 2012

### rcgldr

If there is no net torque, then you'd have to know all of the actual torque values except for one of them in order to determing the value of that one remaining torque value.

In the case of a car coasting, normally the car would be slowing down due to friction in the drive train and rolling resistance. If the car was going slightly downhill with the end result that speed was constant while coasting, then the net torques on the tires and on the drive shaft would be zero.

5. Jan 12, 2012

### keithlaw

"If the car was going slightly downhill with the end result that speed was constant while coasting, then the net torques on the tires and on the drive shaft would be zero."
Great! That is what I want to know. Thank you very much.

But if I put my finger into the center of the wheel, the wheel is going to twist my finger, right? Then there should be a torque, right? Then where does this torque come from???

6. Jan 12, 2012

### Lsos

That's the same effect as if you tried to grab onto a passing train. It's going to put a force on you.

It comes from the fact that the speeds of the two bodies (wheel/finger or train/you) are unmatched, and if you put them in contact then they will try to macth.

How hard it actually twists you finger depends on many factors...how soft your finger is, how wide it is, how hard you are pressing it into the wheel, how fast it's spinning, etc. Essentially it's the same as trying to determine how hard the train will pull on you. There are many factors involved. If you play your cards right, you might even be able to jump onto it and survive. If you play your cards wrong, you could end up a stain on its windshield.

7. Jan 12, 2012