Sometimes it is difficult to come up with new labs. Ideally, a lab should show use some of the basic physics principles as well as have something the students can measure. What to do with circular motion? I don’t know how I forgot this, but here is a lab I used to do as an undergraduate student. I also like it because it doesn’t really need fancy stuff like PASCO probes or anything. The basic idea is that a small mass is swung around in a circle with the tension in the string controlled by hanging a mass on the other end. Here, let me show you.

Circular Motion Lab from Rhett Allain on Vimeo.

Now for the physics. First, here is the set up.

I used a glass-rod to run the string through and the mass at the end of the string that swings around is a rubber test tube stopper. Finally, there is a little piece of blue tape on the string at the bottom of the glass. This tape helps me keep the length of the string constant. Now for a force diagram of the stopper at the instant shown.

The net force on the mass is not the zero vector, this is because the mass is accelerating. A mass moving in a circle has an acceleration of v^{2}/r. If I call the x-direction the horizontal, then I can write the components of force as:

I hate writing F_{string}. Let me look at a force diagram for the mass at the bottom of string (mass-2).

Now I can write down the force equation for mass- (note the hanging mass is not accelerating):

Ok, back to mass 2. If I wanted, I could use the y-equation to solve for the angle the string is above the horizontal.

Ok, now on to the x-direction. First, in a lab a student wouldn’t measure the velocity of mass-2. Instead they would (or could) measure the period of the rotating mass. To connect period and velocity, think about how long and how far it goes in one revolution. The how long is the period. The how far is the circumference. The velocity (magnitude) is:

The radius of the circle is not easy to measure, however I can measure the length of the string (L). From the diagram above, the radius of the circle of motion would be:

So the velocity (magnitude) would be:

Now putting this stuff in the x-direction equation:

This last equation relates stuff that can be measured by students. You don’t need to actually measure the angle. For the lab, I would have the students change the length and measure the new period. Do this several times and plot T^{2} and L. This should be a straight line. Also, if the period squared is on the vertical axis, then the slope should be:

For a bonus, they can use a camera and measure the angle the string makes with the horizontal.