Search: Special Relativity

Students take the inner product of vectors that lie on the spacetime axis to show that they are orthogonal. To do the inner product, students much use the Minkowski metric.

Kinesthetic

5 min.

Time Dilation Light Clock Skit

Special Relativity Time Dilation Light Clock Kinesthetic Activity

Students act out the classic light clock scenario for deriving time dilation.

Homework

Events on Spacetime Diagrams

Special Relativity Spacetime Diagram Simultaneity Colocation Theoretical Mechanics (4 years)

1. Which pairs of events (if any) are simultaneous in the unprimed frame?
2. Which pairs of events (if any) are simultaneous in the primed frame?
3. Which pairs of events (if any) are colocated in the unprimed frame?
4. Which pairs of events (if any) are colocated in the primed frame?
For each of the figures, answer the following questions:
1. Which event occurs first in the unprimed frame?
2. Which event occurs first in the primed frame?

Small Group Activity

5 min.

Events on Spacetime Diagrams

Theoretical Mechanics 2021

Special Relativity Spacetime Diagrams Simultaneity Colocation

Students practice identifying whether events on spacetime diagrams are simultaneous, colocated, or neither for different observers. Then students decide which of two events occurs first in two different reference frames.

Small Group Activity

30 min.

Visualization of Divergence

Vector Calculus II 23 (12 years) Students predict from graphs of simple 2-d vector fields whether the divergence is positive, negative, or zero in various regions of the domain using the definition of the divergence of a vector field at a point: The divergence of a vector field at a point is flux per unit volume through an infinitesimal box surrounding that point. Optionally, students can use a Mathematica notebook to verify their predictions.

Small Group Activity

120 min.

Box Sliding Down Frictionless Wedge

Theoretical Mechanics (4 years)

Lagrangian Mechanics Generalized Coordinates Special Cases

Students solve for the equations of motion of a box sliding down (frictionlessly) a wedge, which itself slides on a horizontal surface, in order to answer the question "how much time does it take for the box to slide a distance \(d\) down the wedge?". This activities highlights finding kinetic energies when the coordinate system is not orthonormal and checking special cases, functional behavior, and dimensions.

Small Group Activity

60 min.

Gravitational Potential Energy

Mechanics Gravitational Potential Energy Zero of Potential Introductory Physics

Students examine a plastic “surface” graph of the gravitational potential energy of an Earth-satellite system to explore the properties of gravitational potential energy for a spherically symmetric system.

Lecture

120 min.

Ideal Gas

Thermal and Statistical Physics 2020

ideal gas particle in a box grand canonical ensemble chemical potential statistical mechanics

These notes from week 6 of Thermal and Statistical Physics cover the ideal gas from a grand canonical standpoint starting with the solutions to a particle in a three-dimensional box. They include a number of small group activities.

Lecture

120 min.

Fermi and Bose gases

Thermal and Statistical Physics 2020

Fermi level fermion boson Bose gas Bose-Einstein condensate ideal gas statistical mechanics phase transition

These lecture notes from week 7 of Thermal and Statistical Physics apply the grand canonical ensemble to fermion and bosons ideal gasses. They include a few small group activities.

Lecture

120 min.

Boltzmann probabilities and Helmholtz

Thermal and Statistical Physics 2020

ideal gas entropy canonical ensemble Boltzmann probability Helmholtz free energy statistical mechanics

These notes, from the third week of Thermal and Statistical Physics cover the canonical ensemble and Helmholtz free energy. They include a number of small group activities.