# Tutor profile: Anu G.

## Questions

### Subject: Physics (Newtonian Mechanics)

What is kepler's 3rd law

Kepler's third law: The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. The el cheapo explanation: Planets that are farther from the sun take longer to complete a revolution around it. The honest-to-goodness explanation is the same as the el cheapo explanation, except we're a bit more precise about "farther from the sun" and "longer to complete a revolution". What do we mean by how far a planet is from the sun, given that the orbit isn't circular? Simple, you take the distance at the farthest point, and the distance at the closest point, and just use their average. That's the length of the "semi-major axis". How much longer is longer? Does a planet four times farther take four times as long? Twice as long? Sixteen times as long? Turns out, it takes eight times as long. The cube of distance is proportional to the square of the time a revolution takes. So if you know the distance and orbital time of one planet, you can find the orbital times of all other planets knowing their distances, or vice versa. And that's what Kepler's third law means.

### Subject: Physics (Electricity and Magnetism)

Explain Lenz's law

So it starts with electromagnetic induction. Simply put, a changing or moving magnetic field generates an electric field, and a changing or moving electric field generates a magnetic field. This is simple enough - it's how electromagnets work, and how we generate electricity using spinning turbines. You can set up two circuits held close to each other in the same plane (like your hands just before you clap), one attached to the AC mains and one with no power source at all. The AC power going into the first circuit creates a constantly changing current in the first circuit This changing current generates a changing magnetic field around the current in the first circuit This, in turn, generates an electric current in the second circuit This induced current generates its own magnetic field around the current in the second circuit Lenz's Law simply states that the magnetic field generated by the induced current in the second circuit will oppose the magnetic field that was produced by the first circuit. This also means that any induced current in the second circuit will move in the opposite direction to the original current, because the magnetic field generated by a current moves in a predictable way around that current (give a thumbs up sign with your right hand - if the current moves in the direction of your thumb, the magnetic field that it generates always follows the path of your fingers around the current). It's all tied up in conservation of energy - if the two fields moved in the same direction, they would constantly reinforce each other and you'd have free energ

### Subject: Calculus

Let's start with something fundamental! What is a derivative?

In algebra you learned to calculate the slope of a straight line. y = mx + b, right? m is the slope. But what about a curved line? Then the slope isn't constant. It changes: it's higher when the line is steeper, and lower when the line is flatter. So instead of a single number, the slope is a function of x. At any given x, your line has a certain y value, and a certain slope. Calculus is the set of math tools that allow you to find the slope function from the original function, or the original function from the slope function. The derivative is finding the slope function. For example the derivative of y=x2 is y'=2x. That means a basic parabola has a slope of 2x. Later you will learn about integrals, which are the opposite: they allow you to reverse the derivative, finding the original function from the slope function.

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