Torque of a wheel in space

localrob

I know if I apply a force(perpendicular to he radius) to a wheel to rotate it, I am applying a torque. I change the wheel's angular acceleration, thus creating a torque.
I can find the direction of a torque via the right hand rule.

If there is a wheel spinning in space where there are no forces acting on it, does the wheel still have a torque?
([tex]\tau[/tex] = L[tex]\alpha[/tex])
Doesn't the wheel still have an angular acceleration?

I'm afraid I've been thinking about all of this too much and am beginning to confuse myself.

russ_watters

In space or not, if there is no force acting on a wheel, there is no torque and no angular acceleration.

localrob

ok, I think I was getting the linear acceleration and angular acceleration confused.

A spinning wheel will have centripetal and tangential acceleration, but it will not have angular acceleration b/c there is no change in angular velocity.

So not all spinning objects have angular acceleration or torque.

russ_watters

Correct, with the caveat that I wouldn't say "the wheel" has a centripetal acceleration - different points on the wheel will have different centripetal acceleration and a point at the center will have none.

Phrak

Push on the center of mass of an object with a force, and you've applied torque. Doesn't sound as if it makes sense does it?

Torque is defined as a force acting about a point. You can choose any point you like. It doesn't have to be the center of mass. If the force is one pound, and the point of interest is one foot from the line of force, the torque is one foot-pound.

Take a wheel that is at rest and not spinning. If you push on the rim, it will both spin and obtain a translational velocity. If you don't want it to give it a velocity, you apply an equal and opposite force on the opposite side of the rim. This is called a Force Couple. It's the intuitive idea alot of use have about what is torque, before we lean the weird definition.

sganesh88

You're almost right. No point of an object spinning with uniform angular velocity has tangential acceleration. Only if you apply a torque, does tangential acceleration arise.

Archosaur

True, but you have to admit, it is confusing. Acceleration is the change in velocity over time, and tangential acceleration is the change in tangential velocity over time, but tangential velocity doesn't include direction like regular acceleration does. It's just speed.

So, many thanks to the jerk who decided against calling it tangential speed.