Course Material

Characteristics of an LC circuit using Equipartition

Submitted by shaviv on Tue, 2011-12-27 11:25
An LC circuit is one which has a capacitor and an inductor connected to each other. It exhibits oscillations just like a mass on a spring (a harmonic oscillator). In fact, the analogy is quite accurate with the capacitor playing the role of the spring and the inductor playing the role of the mass inertia.

Just like any harmonic oscillator, we can use equipartition to estimate the energy and frequency of oscillations using equipartition.

The average energy in the capacitor is:

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Estimating the Size of the Hydrogen Atom (i.e., Bohr's Radius) using Equipartition

Submitted by shaviv on Tue, 2011-12-27 01:08
The standard way to obtain the size of the hydrogen atom, also known as Bohr's radius, is to solve Schrödinger equation for the hydrogen atom. This is a somewhat detailed calculation requiring the usage of generalized Laguerre polynomials and spherical harmonics. We can however bypass it, if we are only interested in an estimate of the hydrogen atom.

One method which we don't follow here, is to estimate the size of the atom using dimensional analysis. Instead, we shall do so using the principle of equipartition.

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Stokes Drag (free fall + linear air drag force)

Submitted by shaviv on Sun, 2006-11-12 02:02
Let us study a somewhat more complex case of motion in a gravitational field. Instead of just the force of gravity, let us add a drag force which is proportional to the velocity, that is:
$$ {\bf F} = - \alpha {\bf v}. $$

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A short history of Mechanics

Submitted by shaviv on Tue, 2006-08-29 22:28
If you are reading these lines, you either accidentally stumbled upon or deliberately looked for Mechanics and Relativity course notes. These notes are used in the first year physics major's classical mechanics course. They were prepared over the course of 3 semesters whilst I was teaching Classical Mechanics and Special Relativity for first year Hebrew University physics undergrads. If you're a first year student in a university which respects itself, these notes are probably suited for you, though don't be surprised if some of the curiculum is different from your course—different physics departments place different emphases.

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A few words on the course

Submitted by shaviv on Sun, 2006-08-20 20:28
If you are reading these lines, you either accidentally stumbled upon or deliberately looked for Mechanics and Relativity course notes. These notes are used in the first year physics major's classical mechanics course. They were prepared over the course of 3 semesters whilst I was teaching Classical Mechanics and Special Relativity for first year Hebrew University physics undergrads. If you're a first year student in a university which respects itself, these notes are probably suited for you, though don't be surprised if some of the curiculum is different from your course—different physics departments place different emphases.

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Classical Mechanics and Relativity / Course Notes

Submitted by shaviv on Sat, 2006-08-12 17:29
The following are the course notes for Classical Mechanics and Relativity. The intended level is that appropriate for physics majors in any university which respects itself.

As of October 2006, the notes are still incomplete.

Notes also exist as a scanned handwritten hebrew version.

Classical Mechanics

  • Introduction
  • Newton's laws, forces
  • Momentum
  • Energy
  • Center of Mass & Angular Momentum
  • Harmonic Motion

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The Twin Paradox

Submitted by shaviv on Fri, 2006-08-11 17:34
The twin paradox is very interesting as it demonstrates the incompleteness of the sepecial theory of relativity. Specifically, the theory is inadequate to describe accelerating coordinate frames.

The Paradox

Let's consider two twins. The first, twin A, stays on Earth while his twin brother, twin B, leaves Earth for a voyage. As measured by twin A, the voyage is composed of two segments. Over the first segment, twin B travels away from earth at a speed v, for a duration of ΔtA long, over the second segmant, twin B approaches earth with the opposite speed

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