Activity: Time Dilation

Theoretical Mechanics (4 years)
What students learn - Clocks moving relative to you run slower than your clock - Proper time is measured by the observer for whom the events are all at the same spatial coordinate (colocated)

• face Lorentz Transformation (Geometric)

face Lecture

30 min.

Lorentz Transformation (Geometric)
Theoretical Mechanics (3 years)

In this lecture, students see a geometric derivation of the Lorentz Transformation on a spacetime diagram.
• assignment Events on Spacetime Diagrams

assignment 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?

1. 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?

• group Events on Spacetime Diagrams

group Small Group Activity

5 min.

Events on Spacetime Diagrams
Theoretical Mechanics 2021

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.
• assignment_ind Dot Product Review

assignment_ind Small White Board Question

10 min.

Dot Product Review
Static Fields 2023 (8 years)

This small whiteboard question (SWBQ) serves as a quick review of the dot product. It is also an opportunity to help students see the advantages of knowing many different representations of and facts about a physical concept.
• group Applying the equipartition theorem

group Small Group Activity

30 min.

Applying the equipartition theorem
Contemporary Challenges 2021 (4 years)

Students count the quadratic degrees of freedom of a few toy molecules to predict their internal energy at temperature $T$.
• group Sequential Stern-Gerlach Experiments

group Small Group Activity

10 min.

Sequential Stern-Gerlach Experiments
Quantum Fundamentals 2023 (3 years)
• group Visualization of Divergence

group 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.
• accessibility_new Curvilinear Basis Vectors

accessibility_new Kinesthetic

10 min.

Curvilinear Basis Vectors
Static Fields 2023 (10 years)

Curvilinear Coordinate Sequence

Students use their arms to depict (sequentially) the different cylindrical and spherical basis vectors at the location of their shoulder (seen in relation to a specified origin of coordinates: either a set of axes hung from the ceiling of the room or perhaps a piece of furniture or a particular corner of the room).
• assignment_ind Curvilinear Coordinates Introduction

assignment_ind Small White Board Question

10 min.

Curvilinear Coordinates Introduction
Static Fields 2023 (11 years)

Curvilinear Coordinate Sequence

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.
• face Basics of heat engines

face Lecture

10 min.

Basics of heat engines
Contemporary Challenges 2021 (4 years) This brief lecture covers the basics of heat engines.

Learning Outcomes