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.

1. 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?

      

2. 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?

      1. 

      2. 

      3. 

Student consider several curves on a spacetime diagram and have to judge which curves could be worldlines for an object.

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.

See also the following more detailed problem and solution: Effective Potentials: Graphical Version

An electron is moving on a two dimension surface with a radially symmetric electrostatic potential given by the graph below:

1. Sketch the effective potential if the angular momentum is not zero.
2. Describe qualitatively, the shapes of all possible types of orbits, indicating the energy for each in your diagram.

In this lecture, students see a geometric derivation of the Lorentz Transformation on a spacetime diagram.

First, students are shown diagrams of cylindrical and spherical coordinates. Common notation systems are discussed, especially that physicists and mathematicians use opposite conventions for the angles \(\theta\) and \(\phi\). Then students are asked to check their understanding by sketching several coordinate equals constant surfaces on their small whiteboards.

This is the first activity relating the surfaces to the corresponding contour diagrams, thus emphasizing the use of multiple representations.

Students work in small groups to interpret level curves representing different concentrations of lead.

Students use chain rule diagrams to construct a multivariable chain rule in terms of differentials.