The Physics of Spinning my Car Keys

The Physics of Spinning my Car Keys

            As I was walking into the library the other day, I noticed that I have a habit of spinning my car keys around my finger. At the time I was studying for the angular motion test (go figure) so I started thinking about all of the forces involved in me spinning my keys around my finger. The first thing I thought of was that I am applying a perpendicular force to my car keys which starts the initial motion. Once the motion has started, the radial force exerted on the mass of the keys in the direction of the axis of rotation keeps the keys going in a circular motion. My keys are approximately 0.115m in length and upon timing myself, I found that it takes approximately 0.5s for my keys to complete one full rotation around my finger. Now that I have obtained this data, I can calculate some interesting values regarding my funny habit. Based on the data I obtained in my perfectly controlled experiment (obviously), I calculated that my keys are spinning at a rate of approximately 12.57 radians per second. From that I calculated that the tip of my keys was rotating at 1.45 m/s which is 3.24 mph. I found this value very interesting because looking at my keys it seems like they are rotating a lot faster than they are just to the naked eye. I think that this is because it is such as small rotation that takes such a short amount of time that the mind assumes it is spinning faster.

            Another interesting aspect of this is that my keys have many different keys and key chains attached to them of various sizes and masses. Since I am applying a uniform force to the key chain, I noticed that the more massive object attached to the keychain move much slower than the smaller objects. This is because since the force is uniform, and force= mass x acceleration. Therefore, the more massive objects will have a slower acceleration than the larger objects as long as we are assuming that the force I am applying to the keychain is uniform to all of the objects.