Why is Coriolis effect equals Zero in my question?

Question

I got a question in my homework.
A disc turns around with angular velociy W. There is a slot from its center which a spring connected. to the spring edge a little mass connected. There is no friction in the question. in the middle of the process while the spring becomes longer the Book says there is no CORIOLIS Forece on the little mass but only Centrifugal Force and the force of the spring. Why?
I understand that there is a velocity of the mass outside the disc in a straight line, so the Cross Product of the V and W is not Zero? Am I wrong?

Answer 1

I'm not entirely sure about the geometry of your situation, but the Coriolis effect is simple to understand, in principle: in rotational equilibrium, everything turns around the center with the same period τ, but at different radii they describe larger or smaller circles, moving a distance 2 π r in this time. Thus the speed is given by v = 2 π r / τ = ω r, where we define ω = 2 π f = 2 π / τ.



The Coriolis effect simply says "when you move further away from the center, you go from an environment where everything is moving with you at speed ω r to an environment where everything is moving at speed ω (r + dr), and so you appear to be going 'backwards' at a speed ω dr in this new reference frame." (Of course, when I speak of directions here I mean the angular direction, not the radial direction.)



Now, if the slot goes radially too, then this effect is very simple to understand: if the mass is forced by geometry to sit inside the slot, then the Coriolis force is balanced precisely by a constraint force which says "no, I'm going to accelerate you by the ω dr that you need to remain in rotational equilibrium at your new radius." There is no Coriolis effect because the Coriolis force is balanced out. Does that make it clear?



There would also be no Coriolis effect if the groove went circularly around the disc in the angular direction, since the mass couldn't "get to" the higher radius. But in your case, the mass can "get to" the higher radius, it just can't "fall behind" the way it naturally wants to.

Answer 2

Unless you have movement to or from the center, there would be no Coriolis force. (Drostie does a good job of explaining the dynamics of the force.) If the angular velocity were constant, then the spring would find an equilibrium point, and there would be no movement along the slot, and so no Coriolis force. If there were changes in angular velocity, then you would have movement in the slot and there would be a Coriolis, even if it were balanced by the constraining force of the slot. But the problem could also be telling you to ignore those calculations when there is movement to simplify the situation.

Answer 3

It shows that the gases and liquids on this planet have an inherent momentum that is imparted to them due to the Coriolis effect

Answer 4

Maybe they mean the force is negligible (so the problem is manageable).