Oftentimes the best way to learn something is to teach it. I’ve decided to try this approach to study for my 2.003 test coming up.
WARNING WARNING WARNING!!! Physics content ahead! If you’re afraid of physics, well, frankly, keep reading because you may just learn something important. If you like physics, well keep reading, because you’ll enjoy it. If you don’t really care, stay for the pretty pictures, mmmk? Mmmk.
Alright here’s the problem as its posed to us:
A wheel of diameter R, consisting of a thin uniform rim of mass M and six thin uniform spokes mass m, is released from rest at the top of a hill of height h.
What is the angular velocity of the wheel when it reaches the bottom, assuming that it rolls without slipping?
I’ve played with my tablet and written up the answers nice and pretty-like (in color!). Before you look at that though, let’s do a quick game plan.
1) Energy. Since the wheel starts high and ends low it looks a lot like we can use energy. There’s nothing but gravity doing work so we can use conservation of energy. Everything in orange is energy. Remember, energy before equals energy after. That extra term on the right that you may not be familiar with is called the “Rotational Energy” and involves the moment of inertia and omega (angular velocity (what we’re solving for!)).
2) Moment of Inertia. We need to find it. For the wheel. This involves finding the moment of inertia for the rim and adding the inertia for each of the 6 spokes. How do we find the spokes’ moments of inertia? Parallel axis theorem!
3) Putting it all together. Plug your moment of inertia into the energy equation and solve for angular velocity omega.
Here’s my solution:
This is just one of many problems I’m reviewing and going over while studying for the test I have in this class on Wednesday. My current strategy is to just shove everything into energy and angular momentum equations until I get the variables I want. We’ll see how this works.
Back to coloring!