Just to be clear, if we let a stopwatch run for 10 seconds and attach a line connecting the sun to Earth and a line connecting the sun to Jupiter then they will both trace the same area as each other.
I saw an explanation for why Jupiter has a slower tangential velocity in its orbit compared to inner planets and it stated:
"Remember that by Kepler’s second law, the planets each sweep-out the same area in the same amount of time. The outer planets’ elliptical orbits are considerably larger...
Radians are dimensionless. So as your intuition would tell you the correct units for rotational energy, which is an energy, are joules or N.m.
Taken from Graham Kemp's response in https://math.stackexchange.com/questions/803955/why-radian-is-dimensionless
"Thus the radian measure of angle as...
A little confused about the applied vs resultant bit too. Having a hard time seeing the gravitational force on an orbitting planet as resultant but not "applied". Probably an issue with definitions I'm not getting.
Unless its saying that the centripetal is generally resultant. In the case of an...
I'm going to enter graduate school in August and I read in an article title something like "Some number of things I wish I knew before going into grad school" that having a way to keep track of all the papers you've read is endlessly valuable. Incidently I lost the article and don't know the way...
Strictly in terms of your ranking, condensed matter theory is very very different than quantum error correction. With quantum computing, if the adviser doesn't have "quantum computing" somewhere on the lab website then I'd seriously question working with them for the 4+ years of research.
There...
I'm actually in the same boat as you. Choosing between schools and such.
Unfortunately, this question has a crappy answer. How far is too far? ONLY you can decide that. How far are you willing to go from your primary interest. Chances are if the subject is within the same realm, then you can...
I'd recommend taking a few intro programming classes. If there's an option for a minor in Computer Science, its something to look into. Be careful though. Usually these classes take a good chunk of time because of projects. If you're looking for something to accompany a physics degree, computer...
Starting out I think you should absolutely convert it to English in your head. It slows you down and makes you notice every detail in the equation. It also makes it easier to communicate mathematical ideas to someone in a conversation! Rarely the ideal way to do it but sometimes you have to...
Knowing both ways is helpful. I think knowing how the non-calculus methods are derived from the calculus methods are absolutely beneficial. In general knowing how the less complex methods are derived from the more complex methods is an incredibly valuable and necessary skill. It's one that can...
I can tell you my eyebrows are NOT symmetrical. There's a sq cm of it on my left eyebrow that the grain runs north where the rest runs to the side as normal. The perfection of nature.
There have been a few tests where I feel like I should have failed but have gotten A's on because the rest of the class did worse that me... Not exactly encouraging because I want to master the material; not just do better than some random set of people.
A great introduction is the Feynman Lectures. They follow a slightly different order than one that you'll find in courses which is beneficial because when/if you take those it will be a fresh take on the material. The Lectures can be semi-expensive on their own in physical form (unless you visit...