Learning about logarithms is one of those times in math class where you wonder if this will ever be useful in any way. I see lots of students struggle with topics like logs, since they can seem abstract and they aren’t obviously useful. But I’m here to explain why they are actually incredibly important and describe so much of the world we live in! Let’s take a look at an example from chemistry and physics that shows just how powerful logs can be - the Arrhenius Equation.

Tags: physics, math

Many people, often family members, ask me how astronomy and physics differ. Since I am studying solar physics, I usually give the “short answer”-- that astronomy is just a specific branch of physics. However, there are widespread cultural differences that make the “long answer” rather more involved.

Tags: physics

##### Much like Bill Murray in Groundhog Day, those who take many ETS physics tests may develop a feeling of déjà vu...

ETS is many things: creative is not one of them. It uses the same questions over and over and over. Therefore, the best way to study for standardized tests of any kind (especially in physics) is to take lots of practice tests

Last time on our physics tutoring blog, we conducted an experiment to investigate the influence of the moment of inertia on rolling motion. We started with two objects that had the same shape, but very different size and mass. Starting from rest, we then set them both rolling down a ramp, to see which one would reach the bottom first. The objects had different values for the moment of inertia, but nonetheless reached the finish line at the same time. So, we resolved to try a second experiment, repeating the first experiment but with two objects that have different geometries. Again, to keep it simple, we’ll stay focused on objects that have a circular cross-section, and that are easily found lying around the house. This time, we’ll pit the marble against a roll of masking tape. The roll of tape is larger and heavier than the marble, but from the analysis of our previous experiment we might expect the mass and size not to influence the outcome. Let’s see what happens:

#### And here is a close-up of the finish line.

We have a winner! The marble beat the tape by a clear margin. So, the geometry of the rolling objects is definitely a deciding factor in this race. Let’s take a look at the math, and compare with the previous experiment. For the roll of tape, we can approximate the shape to be a ring, which has a moment of inertia of I = MR2 when rotated about its center. Using the subscript m to denote the marble and the subscript t to denote the roll of tape, we can set up the energy balance equations in the same way as we did before:

Tags: physics

##### Not that kind of inertia.

Sometimes, when you are sitting in a physics class staring at an intimidating wall of math, it can be easy to lose sight of the fact that the laws of physics originated as hypotheses to explain observations in the real world. Whether it was Newton getting bopped on the head by an apple, Galileo dropping stuff off the Tower of Pisa, or Franklin electrocuting himself with a kite, there was often an experiment that preceded and informed the mathematical formulation of a physical law. As a physics tutor in Cambridge, I find that it’s easier for my students to stomach the math if they’re able to imagine what it means, if they can figure out the physical consequence hidden behind the equation. For example, when looking at Newton’s second law (F = m a), I imagine pushing on a box. When I push (apply a force) on the box (a mass), it starts moving (it accelerates). If I push harder (apply a larger force) on the box (still the same mass), it starts moving more quickly (a larger acceleration). And while thought experiments are great, real experiments are more fun! Today we will set up some experiments to investigate one of the more abstract concepts in classical mechanics: the moment of inertia.

Tags: physics

##### Sometimes, you just do what you gotta do.

Learning to take standardized physics exams, like the AP Physics exam or the SAT Physics Subject Test, is not unlike trying to become fluent in a foreign language. Both follow highly idiosyncratic logic and are best learned through practice. (And believe it or not, standardized physics exams have less to do with physics than physics aficionados would like.) Now before you combust, hear me out. I’m not saying that the tests don’t contain physics, or that understanding physics won’t help you; I’m saying that it is only one of many factors in these exams.

Tags: physics

Tags: physics