How to calculate torque of a rotating wheel at constant angular speed?

[sixelements]

Suppose there is a rotating wheel at constant angular speed, i.e, 1000 RPM (Revolution Per Minute). What is the torque of Earth at certain location? The equator should have the maximum torque value.

I find the angular speed w by 1000 x 2Pi rad x 1 / 60s = 104.71 rad/s
Assume M is the mass of the rotating wheel. R is the radius.

Because it's revolving at a constant angular speed, the tangential angular acceleration (alpha t ) is zero.

I can get the inertia (I) and kinetic energy K by formulas. Then, I'm kind of stuck how to find out the torque?
Read through the rotation chapter of physics book have twice, checked all the examples without success.

What am I missing here?

Thanks in advance.

 

[SteamKing]

The presence of a torque will cause a change in the angular velocity of a wheel. (In this case, torque and its effect on angular velocity is analogous to the effect a force has in changing the velocity of a mass in rectilinear motion.) If a body is rotating with a constant angular velocity, the net torque is zero.

As to What is the torque of the Earth, you will have to explain what you are looking for in more detail.

 

[gsal]

I think the only torque involved is the one to overcome friction and that's it...at this point, the mass of the wheel is irrelevant.

If you think the gravity of Earth is helping turn the wheel, I presume the shaft of the wheel is horizontal correct? In any case, gravity does not help at all...after all, for every piece of mass coming down in one half of the wheel, there is another one going up on the other side and so, the effect of gravity is a wash.

...if non of this answers your question...then I don't know what in the earth you are talking about :-)

 

[BobG]

Suppose there is a rotating wheel at constant angular speed, i.e, 1000 RPM (Revolution Per Minute). What is the torque of Earth at certain location? The equator should have the maximum torque value.

I find the angular speed w by 1000 x 2Pi rad x 1 / 60s = 104.71 rad/s
Assume M is the mass of the rotating wheel. R is the radius.

Because it's revolving at a constant angular speed, the tangential angular acceleration (alpha t ) is zero.

I can get the inertia (I) and kinetic energy K by formulas. Then, I'm kind of stuck how to find out the torque?

I'm at a loss as to what you're trying to ask. The Earth's gravity will have no effect on how fast the wheel is spinning. If the wheel's axis is aligned with the Earth's radius and the wheel is rotating at a constant speed, the angular acceleration and the torque is zero.

Or, since you ask about the torque of the Earth, are you asking about precession?

http://hyperphysics.phy-astr.gsu.edu/hbase/rotv2.html

 

[rwisz]

To calculate the torque of a rotating wheel at constant angular speed, we can use the formula: torque = moment of inertia x angular acceleration. In this case, since the angular acceleration is zero, the torque would also be zero. This means that the torque of the wheel at any point on its surface would be zero, including at the equator.

The torque of the Earth at a certain location can be calculated using the formula: torque = force x distance. However, since the force of the Earth's rotation is not constant and varies with latitude, it is not accurate to say that the equator has the maximum torque value. The torque of the Earth at a certain location can also be affected by other factors such as the shape and density of the Earth's interior. Therefore, it is not possible to accurately determine the torque of the Earth at a specific location without more information.