Physics Notes

The following are notes for Physics students, written by Archie Paulson.

Math

• Trigonometry – review, graphs, formulas, etc
• Vectors – unit vectors, dot product, cross product
• Differential Equations – two diff-eq’s we need to solve in Physics 1 and 2
• Useful Approximations – the binomial and small angle approximations

Problem Solving

• Kinematics Problems – solution procedures for 1D and 2D kinematics
• Dynamics and Free-body diagrams – how to solve dynamics problems with the FBD
• Symbolic Problem Solving – why the pros use symbols rather than numbers
• Dimensional Analysis – double check your work and get to the heart of the Physics

Experiment & Computation

• Computational Physics – using the Jupyter Notebook
• Measurement Uncertainty – how to propagate uncertainty

Theory - going further

• Gravity Integral
  • This work shows that outside of any spherically symmetric mass distribution (such as a planet) the gravity field is identical to that of a point particle with equal mass. It also shows that inside any spherically symmetric mass shell (such as a planet with a concentric spherical cavity), gravity is zero throughout the interior.
• Projectile Orbit
  • A projectile in a uniform gravity field follows a parabolic path. But according to Kepler’s First Law the projectile is actually orbiting the center of the Earth in an ellipse. You can show that these curves are the same with a little algebra.
• Multiparticle Dynamics
  • An external force may accelerate and rotate a system of particles.

Last modified in September 2025 by Archie Paulson.