Do Centrifugal and Centripetal Forces Exist in Outer Space?

[Dale]

- but it does not exist on objects that are moving with an angular rotation about the centre axis with an equal and opposite rotation to that of the frame. (because such objects are in fact not rotating and not moving at all).

well you could say they DO have a centrifugal force acting on them, but it's of magnitude zero.

The centrifugal also acts on such objects. Its value is mω²r, so it is only equal to 0 for r=0.

 

[YellowTaxi]

I would say that the centrifugal force does exist in the rotating reference frame.

The centrifugal also acts on such objects. Its value is mω²r, so it is only equal to 0 for r=0.

No,
If you move with an ω numerically equal to the ω of the rotating frame but in the opposite direction, you aren't moving at all. And then mrω² for all values of r is zero. Even though from the rotating frame you seem to have an angular speed ω, you in reality are standing still.

That's why I think the rules for statics will work fine on a rotating frame , but anything moves at all [in any direction] and it all gets bizarre, and Newton flies out the window.

 

[Dale]

No,
If you move with an ω numerically equal to the ω of the rotating frame but in the opposite direction, you aren't moving at all. And then mrω² for all values of r is zero. Even though from the rotating frame you seem to have an angular speed ω, you in reality are standing still.

That's why I think the rules for statics will work fine on a rotating frame , but anything moves at all [in any direction] and it all gets bizarre, and Newton flies out the window.

I think you are thinking about the Coriolis force, which is -2m(ωxv). So it does depend on the velocity in the rotating reference frame.

If an object is stationary in the inertial reference frame then it obviously travels in a circular motion in the rotating reference frame. To travel in a circular motion it must have a centripetal force, which is provided by the Coriolis force. The Centrifugal force, of course, is in the opposite direction of any centripetal force, but the factor of 2 in front of the Coriolis force makes it twice the magnitude of the Centrifugal force resulting in a net centripetal acceleration in the rotating reference frame.

PS sorry, that is confusing to read but I am too sleepy to write more clearly

 

[YellowTaxi]

I think you are thinking about the Coriolis force, which is -2m(ωxv). So it does depend on the velocity in the rotating reference frame.

no I'm not talking about coriolis at all here. We were both discussing mω²r which is not the coriolis force ;-)

If an object is stationary in the inertial reference frame then it obviously travels in a circular motion in the rotating reference frame.

yes , that was exactly my point in my previous post. This object which appears to have circular motion when viewed from the rotating frame will in fact be standing perfectly still in space. The tension in the string (say), or the force from a retaining wall required to hold it there will be zero.

 

[Doc Al]

No,
If you move with an ω numerically equal to the ω of the rotating frame but in the opposite direction, you aren't moving at all.

You aren't moving with respect to the inertial frame.

And then mrω² for all values of r is zero.

No. The ω in the formula for centrifugal force is due to the rotation of the frame; it's not the ω with respect to the rotating frame.

Even though from the rotating frame you seem to have an angular speed ω, you in reality are standing still.

Again, you are at rest with respect to the inertial frame, not the rotating frame.

That's why I think the rules for statics will work fine on a rotating frame , but anything moves at all [in any direction] and it all gets bizarre, and Newton flies out the window.

To be used from a rotating frame, Newton's laws, including their application to statics, must be modified to include all relevant "fictitious" forces.

no I'm not talking about coriolis at all here. We were both discussing mω²r which is not the coriolis force ;-)

You're not talking about coriolis, but you should be. If you are moving with respect to the rotating frame, coriolis force must be considered.

yes , that was exactly my point in my previous post. This object which appears to have circular motion when viewed from the rotating frame will in fact be standing perfectly still in space. The tension in the string (say), or the force from a retaining wall required to hold it there will be zero.

It's certainly true that an object at rest in an inertial frame requires no net force to remain at rest. But if you choose to analyze the situation from the view of the rotating frame, it is certainly moving. Both centrifugal and coriolis forces are at work.

Let's say the frame is moving counterclockwise at angular speed ω with respect to the inertial frame. Thus there will be a centrifugal force = mω²r acting outward. If the object also moves clockwise with an angular speed ω with respect to the rotating frame, there will be a coriolis force = 2mω²r acting inward. Thus, from the rotating frame, there will be a net inward force equal to mω²r. Which makes sense, since from the rotating frame the object is accelerating inward. (No "real" force is required.)