I spent half the class this week lecturing on rotational motion and trying to get across that it really isn’t very different than linear motion. In linear motion we have displacement (x), velocity (v) , momentum (p), and force (F), while in rotational motion we have angular displacement (θ) , angular velocity (ω), angular momentum (L) and torque (τ). We went over moment of inertia and how its the equivalent of mass for linear motion, but varies depending on the object’s shape. The further the mass is from the axis of rotation, the harder it is to rotate since you have to go a great distance in the same amount of time. So a disk with all the mass on the rim, like a bicycle wheel, will be harder to rotate than a solid disk of the same size and mass because some of the mass is closer to the axis of rotation. To prove this we did an experiment with a variable inertia apparatus (bought at cynmar for $16)- basically two plastic disks with cubby holes inside where you can place heavy ball bearings. So you can put all the mass near the center or have it near the outer rim of the disk. You can also change the mass of the disk by putting in more or less balls. The students set up a very shallow ramp and timed how long it took the disks to reach the bottom for various combinations of ball bearings. As they predicted, when the mass was distributed far from the axis of rotation the moment of inertia was high and the disk took longer to reach the bottom of the ramp. If the mass was clumped close to the axis of rotation then it rotated/rolled down the ramp faster. Increasing the overall mass of the disk also increased the moment of inertia and the time to get down the ramp.
I don’t have a bicycle gyroscope so we watched the video by Vertasium Gyroscopic Precession.
And check out this demonstration with toliet paper.