Tutoring Conceptual Physics at RLS

We looked at conceptual problems related to magnetism. The book used by the school doesn’t use equations much. Which seems like a strange approach to me.

I think it would be useful to see something like the Lorentz Force Law which involves the movement of a point charge in a magnetic field and has a cross product.

F=qvxB, where F, v, and B are vectors. The right hand rule can be used with the cross product.

Can look more at this later on, will bring another book.

Newtons and Distance in an equation

Newtons and meters are sometimes related to each other and you can see the relationships within equations.

One such equation is that work is equal to the dot product of force and distance. Force has units of Newtons, distance has units of meters.

There are other equations with both units as well.

Tutoring Physics, Light, Indices of Refraction

We went over some problems with lenses, converging and diverging.

Then spent some time on problems with different indices of refraction. I would usually think of air to water and the behavior if you get mixed up.

Used Snell’s Law and another equation with the velocity of light, c, and the index of refraction.

n= c/v

The index of refraction is about 1 in air and is 1 in a vacuum. It doesn’t (in the context of this class) go below 1.

Tutoring Physics, Dot Products and Cross Products Return

We looked at induced currents, loops, magnetic fields.

Spent some time on the right hand rule.

Also looked at the difference between dot products and cross products. They are important for the current material.

The result of a dot product is a scalar, the result of a cross product is a vector.

One has the sine function in it and the other has a cosine.

So if you took the dot product of two perpendicular vectors, you would get zero.

If you took the cross product of two parallel vectors, you would get zero.

Good not to mix them up. Neither one of them is simply ‘multiplication’, though sometimes they reduce to that depending on the scenario. The cross product will still have a direction in addition to a simple multiplication even with orthogonal vectors.

Two Kinematic Equations Illustrated

I drew this diagram of two equations in physics. I used different colors to show different things. The letter x stands for position, the letter v stands for velocity, the letter a stands for acceleration, and the letter t stands for time. The diagram of the person shows an example of someone starting at a certain position, moving with acceleration, and ending up at another position over an amount of time.

Dibuje este diagrama de dos ecuaciones en física. Use diferentes colores para mostrar diferentes cosas, la letra x expresa la posición, la letra v para expresar la velocidad, la letra a para expresar la aceleración y la laetra t a para expresar el tiempo. El diagrama muestra a un ejemplo de alguien que empieza en un determinado lugar se mueve con cierta aceleración, y termina en otra posición en un determinado tiempo.

Tutoring Physics 2, focusing on components

We went over problems involving electric forces.

For one the horizontal components of the forces canceled out, using that information, we could calculate the sum of the vertical forces and figure out the charges by using Coulomb’s Law.

You can either use trig functions or the Pythagorean Theorem, or a combination, for some of these problems.

Labeling things with subscripts becomes more important once the problems get more complicated.

One problem involved early kinematic equations.

To figure out the units for something, like electric field, you can use the simplest equation you know for that thing and go from there.

“What do nanometers measure?”

You can measure anything with length in nanometers.

The real question maybe should be ‘what do nanometers measure conveniently?’

For example, you could say your height in meters. You could also say it in nanometers.

But to say it in meters, probably gives you a number somewhere under 10. Which is a convenient number to think about.

You can measure something much longer in meters, say the distance from California to NY. But at that point, you’re talking about a very large number and it becomes more convenient to use kilometers since then you can use a smaller number of that unit.

With nanometers, it’s convenient for things like the wavelength of visible light and things at the atomic level.

“How many Planck lengths are in an inch?”

You can ask Google questions like this if you know how to format them correctly.

Tutoring AP Physics, Springs/Conservation of Energy

We started with a problem involving gravitational potential energy, kinetic energy, and elastic potential energy with a mass and a spring.

Work and energy both have units of Joules.

Made an analogy to a trampoline for the spring. Used the concept of conservation of energy. Energy changed forms a few times.

Another problem involved friction and an incline with and without friction. The version with friction was a bit more complicated and required more algebra, factoring out common terms.

For a calculus problem, getting the volume in terms of one variable using a ratio of radius/height was helpful.

Moment of Inertia, Summation of torques

We started by talking about impulse. It is notated using the letter J, not the letter I. In the context of chapter 9, I was the momentum of inertia which has a similar role that mass does for linear motion for rotational motion.

Figuring out the situation of what is going on in a problem can be the most difficult thing. Many times a diagram will help. Thinking about the directions of things can also be useful in getting started. For example with a sliding block and a horizontal restoring force. Also, you can often do problems in several different ways. With the spring and friction, conservation of energy was problem the easiest route.

The other problem had a summation of torques and figuring out the moment of inertia. One mistake would be to not take into account the torque due to the ladder, which can be thought of as a point mass at the center.