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== Day 173 == | |||
--- Eric version --- | |||
'''Angular Momentum''' | |||
So let's talk about this absolute daredevil of a physics concept that I recently stumbled upon: angular momentum. | |||
There are a few things that can go horribly wrong when evaluating a problem. First, counterclockwise rotation is positive, and clockwise rotation is negative. Yep, that's exactly what happens. Now imagine a flywheel spinning counterclockwise about the x-axis. The angular velocity would be how fast it spins. Where would you expect angular momentum to point? Towards the left, the direction of rotation? Nope, it points towards the x-axis. The reason for this is because something in linear algebra called a cross product. Therefore, every time you manage to evaluate angular momentum, you have to use the right hand rule in reverse to find the direction in which something spins. | |||
That just singlehandedly proved how conceptually messy this section of physics is. But don't worry, there's worse: formulas! Before anything we need to talk about gyroscopes. These things are made out of a stand and a flywheel on an extended arm. If you release the arm, it should simply fall down, as can be easily verified. However! If the flywheel was spinning (assuming a frictionless world), the arm will not fall: it will spin around! This phenomenon is called precession and, as you might imagine, this causes quite some complications in our calculations. Now calculus and linear algebra are both involved, and we have a ton of new formulas to recite. Not to mention the moment of inertia, where you literally have to integrate an entire shape for just one value in the formula. Alternatively, you may choose to recite a table of about 12 different shapes. Good luck! | |||
Physics is genuinely fascinating, and I love it with all my heart. It is quite a rare occasion when a few formulas manage to explain the world's phenomena. But when concepts like angular momentum emerge... let's just say doing practice problems is not really an enjoyable process, especially when basically half of them are more difficult than questions in physics competitions. | |||
== Day 172 == | == Day 172 == | ||