Horizontal Circular Motion Problem

[Macroer]

Homework Statement

A stopper is being twirled around(horizontal circular motion), that is attached to a pole with a string.
What happens to the accuracy of Fnet = 4pi^2mrf^2(uniform circular motion equation) as the frequency of revolution of the stopper increases(assuming other variables of kept constant)?

Homework Equations

Fnet = 4pi^2mrf^2

The Attempt at a Solution

As the frequency of revolution increases, the motion of the stopper becomes more horizontal, which means the force of tension comes closer to acting parallel to the horizontal. Since the angle between the string and the horizontal decreases, the vertical component of tension decreases, which results in greater accuracy.

 

[PhanthomJay]

No, that's not correct, but I don't understand how the frequency can change without 'r' changing. As the frequency increases, the horizontal radius must get bigger, so I'm not sure what the problem means by saying that the other variables remain constant. You'd be way off if you held r constant in your calculations, if that's what it means.

 

[kerimek]

Additionally, as the frequency increases, the radius of the circular motion decreases, which also leads to a decrease in the vertical component of tension. Therefore, the accuracy of the equation Fnet = 4pi^2mrf^2 increases as the frequency of revolution of the stopper increases, assuming all other variables are kept constant. This is because the equation takes into account the radius and frequency, both of which decrease as the frequency increases, resulting in a more accurate calculation of the net force.