Why Doesn't a Satellite Rotate with Its Momentum Wheel?

[hamzaaaa]

Dears,

I would like to know a basic thing, why does the Satellite doesn't rotate with the spinning wheel momentum wheel inside it?

 

[mfb]

Why should it? If there is a reaction wheel, the satellite has to maintain its spin, to account for friction. If the relative spin (wheel<->satellite) is constant, angular momentum conservation gives a constant angular velocity of the satellite (usually chosen to be 0).

 

[hamzaaaa]

But for a geo satellite it has an angular velocity equal to Earth's rotation,right?
So the angular velocity is not zero but constant.
This angular rotation is provided by the wheel?

 

[mfb]

That is an angular velocity as seen in the frame of earth, not for the satellite itself.
I don' think I understand what you really want to know.

Satellites do not need those wheels (but they can be useful).

 

[mfb]

That is an angular velocity as seen in the frame of earth, not for the satellite itself.
I don' think I understand what you really want to know.

Satellites do not need those wheels (but they can be useful).

 

[hamzaaaa]

What i want to know is that a satellite having a spinning momentum wheel on 1 axis with constant angular velocity doesn't cause rotation on the satellite itself? But if the wheel speed is increased or decreased it will cause satellite to rotate. Is it explainable with any equation?

 

[mfb]

This is just conservation of angular momentum (in the frame of the satellite). With a frictionless reaction wheel (or a real wheel where friction is countered by a motor), there is no torque on the satellite, so it does not begin to spin.

 

[BobG]

What i want to know is that a satellite having a spinning momentum wheel on 1 axis with constant angular velocity doesn't cause rotation on the satellite itself? But if the wheel speed is increased or decreased it will cause satellite to rotate. Is it explainable with any equation?

With conservation of momentum, you're right that the initial spin up of a momentum wheel will force the spacecraft body to rotate the opposite direction if that's all that happens. However, external actuators (such as thrusters) can also change the spacraft body's spin rate by changing the overall angular momentum of the spacecraft . You spin up the spacecraft body using thrusters, then spin up the momentum wheel to bring the spacecraft rotation back down to zero (although, in practice, the two actions will be virtually simultaneous).

So, in other words, it's not explainable by some equation, but by the physical actions taken to set up the initial conditions. There's no real difference between establishing the momentum wheel's spin and establishing the spin of a spin stablized satellite.

One additional note regarding the title/substance of the thread: There's a subtle difference between a momentum wheel and reaction wheel even if there's no physical difference between them. A momentum wheel has a bias spin that creates a large angular momentum vector. A reaction wheel works around a zero momentum and can spin either direction depending on the torques they're counteracting.