Student handout: Possible Worldlines
Student consider several curves on a spacetime diagram and have to judge which curves could be worldlines for an object.
- assignment_ind Small White Board Question 10 min. A way to project the graph and a way for students to indicate their answers (e.g. with a small whiteboard). Student handout (PDF)
- Search for related topics
Special Relativity Spacetime Diagrams Worldlines Postulates of Relativity
- Speed on a spacetime diagram is inverse slope.
- Object can't travel faster than the speed of light.
- Lightlines have a slope of 1 (when axes are scaled to the same units)
- 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. - group Right Angles on Spacetime Diagrams
group Small Group Activity
30 min.
Right Angles on Spacetime Diagrams
Theoretical Mechanics (4 years) 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. - group Projectile with Linear Drag
group Small Group Activity
120 min.
Projectile with Linear Drag
Theoretical Mechanics (4 years)Projectile Motion Drag Forces Newton's 2nd Law Separable Differential Equations
Students consider projectile motion of an object that experiences drag force that in linear with the velocity. Students consider the horizontal motion and the vertical motion separately. Students solve Newton's 2nd law as a differential equation. - group Mass is not Conserved
group Small Group Activity
30 min.
Mass is not Conserved
Theoretical Mechanics (4 years)energy conservation mass conservation collision
Groups are asked to analyze the following standard problem:
Two identical lumps of clay of (rest) mass m collide head on, with each moving at 3/5 the speed of light. What is the mass of the resulting lump of clay?
- assignment Events on Spacetime Diagrams
assignment Homework
Events on Spacetime Diagrams
Special Relativity Spacetime Diagram Simultaneity Colocation Theoretical Mechanics (4 years)-
Which pairs of events (if any) are simultaneous in the unprimed frame?
Which pairs of events (if any) are simultaneous in the primed frame?
Which pairs of events (if any) are colocated in the unprimed frame?
Which pairs of events (if any) are colocated in the primed frame?
- For each of the figures, answer the following questions:
Which event occurs first in the unprimed frame?
Which event occurs first in the primed frame?
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- group Events on Spacetime Diagrams
group Small Group Activity
5 min.
Events on Spacetime Diagrams
Theoretical Mechanics 2021Special 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. - group Box Sliding Down Frictionless Wedge
group Small Group Activity
120 min.
Box Sliding Down Frictionless Wedge
Theoretical Mechanics (4 years) 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. - group The Hillside
group Small Group Activity
30 min.
The Hillside
Vector Calculus I 2022 (2 years) Students work in groups to measure the steepest slope and direction on a plastic surface, and to compare their result with the gradient vector, obtained by measuring its components (the slopes in the coordinate directions). - group Work By An Electric Field (Contour Map)
group Small Group Activity
30 min.
Work By An Electric Field (Contour Map)
Students will estimate the work done by a given electric field. They will connect the work done to the height of a plastic surface graph of the electric potential. - assignment The Path
assignment Homework
The Path
Vector Calculus I 2022 You are climbing a hill along the steepest path, whose slope at your current location is \(1\over5\). There is another path branching off at an angle of \(30^\circ\) (\(\pi\over6\)). How steep is it?
- Learning Outcomes
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