# Circular Motion

If I wanted to prove that whilst spinning a ball attached by a string in a circle, that:

F = 4 * pi^2 * r / T^2

Where F = force from tension
T = period of one rotation

Ie. Proving that:
F is directly proportional to r
F is directly proportional to m
F is direction proportional to T^-2

How would I measure the force on the string? This is just school physics, so I can't do anything fancy. It'll probably just be someone spinning it in circles above them. The other variables are easy enough, but I need to be able to compare them to force. The only thing I thought of was using the formula F=ma, but the problem is the acceleration is constantly changing so can't be measured.

Thanks A spring would be sufficient.
Just measure the amount it is extended while you swig the weight and how much it extends per amount of force.

What kind of equipment does your school have?
With a spring, a sliding potentiometer, a multimeter, an oscilloscope or an electric graph you could put together a simple measuring/recording rig.
(extra credit! )

A spring would be sufficient.
Just measure the amount it is extended while you swig the weight and how much it extends per amount of force.

What kind of equipment does your school have?
With a spring, a sliding potentiometer, a multimeter, an oscilloscope or an electric graph you could put together a simple measuring/recording rig.
(extra credit! )

Now that I think about it, the teacher mentioned something about the tension being caused by this metal ball at the end of the string. When you spin the string, you actually hold on to this bit of hollow plastic that goes around the string. It's hard to describe, so here's an image. Is there some relationship between F of the bit of the string going in a circular motion, and mg of the weight at the bottom?

Assuming the thread is not attached to the tube, definately!

The weight will pull the thread one way while the ball will pull it the other way.
If either of them pulls harder then the thread will move that way.

You can use the lower ball to tell if the ball has more, less or the same amount of force as the weight.

Great, I'm starting to get somewhere in my understanding of this. So is mg of the lower weight equal to the vertical component of the tension in the string? I need to be able to find out the overall force in the string while it's on an angle.

Be careful here. The ball that is traveling in circular motion also has the force of gravity acting on it.

*edit* sorry just saw that you are thinking about the angle. Draw a free body diagram.