Projectile Motion Trajectory Equation

This comes up every so often. I get a situation (usually, it’s a video analysis problem) in which I can’t rely on the time data. This usually happens when you can see the motion of a projectile, but the middle part (or all of it) is in “slow motion”.

Before looking at the trajectory equation, let’s review what I would normally do for a video analysis. After collection x,y,t data in each frame, I could make two plots. I could plot the horizontal position vs. time. This should be a straight line (because there would be zero acceleration) and the slope of this line would be the horizontal velocity.

The second thing I could do is to plot the vertical position vs. time. This should be a parabola. From the quadratic equation fit of this data, I can find the vertical acceleration.

So, let’s say I can’t do that. How do we get data from an x-vs-y plot? This is the trajectory since it actually shows the path of the projectile. OK, for this case let’s make the following assumptions:

  • It’s a ball. I’m going to call this projectile object a ball. There is no reason for this choice.
  • The ball starts at some position (x_0,y_0).
  • The ball is launched with some initial velocity v_0 and at some angle above the horizontal \theta.
  • In my mind, the ball hits the ground at some point. I’m going to set the ground to be y = 0.
  • Oh, the vertical acceleration is -g, where g = 9.8\text{ m/s}^2.

Now for the physics. First, the initial velocity can be broken into x- and y-components:

v_{x0} = v_0 \cos \theta

v_{y0} = v_0 \sin \theta

For the x-motion, I have the following kinematic equation:

x = x_0 +(v_0 \cos \theta)t

And in the y-direction:

y = y_0 +(v_0 \sin \theta)t - \frac{1}{2} gt^2

In order to get the trajectory equation, I need to eliminate t from these two equations. I’m going to start by solving the x-motion equation for t.

t = \frac{x-x_0}{v_0 \cos \theta}

Now I can substitute this into the y-motion equation.

y = y_0 +\left( \frac{v_0 \sin theta}{v_0 \cos \theta}\right)(x-x_0)-\frac{g}{2v^2_0 \cos^2 \theta}(x-x_0)^2

Oh, notice that the velocity terms cancel in the middle term. Also, we get sine over cosine which is tangent.

y = y_0 +(\tan \theta)(x-x_0)-\frac{g}{2v^2_0 \cos^2 \theta}(x-x_0)^2

This should be good enough. If I make sure that the ball starts at x = 0, then the x-squared term of the quadratic fit in the format of:

y = Ax^2 + B x + C

Where A, B, and C are fitting coefficients. Now, A should be:

A = \frac{g}{2v^2_0 \cos^2 \theta}

So, if I have data and I plot the trajectory, I should be able to find the acceleration. Of course, this assumes that I know the launch velocity and the angle. But wait! I can get the angle from the B term:

B = \tan \theta

But what about the launch velocity? Honestly, I’m not quite sure. I guess if I new the vertical acceleration, I could solve for the launch velocity. Or maybe I could get the velocity from some other source.

Let’s test this stuff out. I could use some video data—but it’s easier to just make a plot in python. Here is a ball launched (with initial x = 0 meters). I get the following for the vertical position vs. time (like I would expect). Here is the code.

That looks good. Now, I’m going to plot two trajectory lines. The first will be calculated in the normal numerical calculation method (same as above but plotting x vs. y instead of t vs. y). The second plot will be the trajectory equation we solved for above. Here’s what I get.

The plots aren’t identical—but I could easily fix that. This shows that the thing works.

Remote Physics Labs

This is not a normal semester. So, how can you move your physics labs to a remote learning environment? Here are some ideas.

What is the goal of a lab?

This is what we should always consider when making any changes to a curriculum. What are we trying to do. Or, in the words of Arnold Schwarzenegger:

“Who is your daddy, and WHAT does he do?”

Kindergarten Cop

So, why do we have labs? Honestly, I don’t know. Here are some thoughts:

  • They gives students a “hands-on” opportunity to explore the physics from their lecture class.
  • Students can get experience with certain pieces of important equipment—oscilloscopes, meter sticks (kidding).
  • The nature of science. How do you learn about science without doing science? In labs, students can design and build their own experiments (ideally).
  • Science communication. This is what a lab report is supposed to do—but even having students share ideas in class can be super useful.
  • More time with physics.

I don’t the answer here. Also, if the lab is a service course for some other major then I guess that other department should tell us what they want out of the lab.

Now for some remote lab ideas.

Online labs

What if students had some type of online lab? Maybe they could play around with some virtual lab equipment to collect data. I’m thinking about the PhET simulators. They have some pretty sweet circuit simulators. Students could build a circuit, measure voltage and current and do a bunch of stuff. Not bad.

There’s also the great Pivot Interactives videos. These are pre-made video experiments with measurement tools built in. Students can use the video and measure stuff like the time it takes a ball to fall or the period of a pendulum. This stuff is really nice.

Oh, there’s also Second Life. Physics labs in a virtual reality. I’m mostly joking, but maybe…

Numerical Calculations

This is the perfect time to have students solve some physics problems with python (or some other method for numerical calculations). I honestly think this is great thing for lab anyway—I’ve used these in classes for a while and they are quite successful.

Here is my numerical calculation jump-start guide.

Give them the data

What if you show a video (or two) of the physics and then just give them the data? So, let’s say you are looking at the magnetic field due to a bar magnet or a wire carrying current. Normally, students would use a magnetic compass to plot the magnetic field as a function of distance.

I could record the compass deflection values for different distances and then let them do the analysis. I don’t think this such a bad option. You can use the labs that you already have and then you just need to include some extra pictures or videos and then a data table.

At home labs

This seems like a great idea, but you might have to be flexible. Suppose you want to study pendulums—surely students can find some string with a mass on it to swing back and forth. They could find the time with their phone. What about the length of the string? This might require a little bit of thinking to get it to work—but I would suspect that most students could do it.

Another option is to have students think up their own labs. Maybe they could take inventory of their supplies and use that. Don’t forget of all the sensors on a smart phone—I’ll suggest PhyPhox as a great app.

Just Enough Physics Video Update

Perhaps you haven’t noticed, but I’ve been trying to make a bunch of physics videos. Oh, sure—I already have a ton of stuff on youtube, but it’s not linear. For my old stuff, I will solve a problem on work-energy and then do electric field stuff and then go back to kinematics. It was just whatever topic came up in class or online or whatever.

I figured I should start over and do a whole physics course—well, not EVERYTHING. No, I would do just enough to get you through the course. I hope you get the title now. Also, this is the title of that self published ebook I wrote a long time ago—since it really is the video version (but updated).

So, where am I now? I’ve got 4 chapters completed. I think it’s a pretty good start. Here are the chapters (as playlists) along with descriptions.

Chapter 1: Kinematics

Notice that I started off by making a title screen and all that cool stuff. I will end up dropping this so that I can make videos faster. Also, in my previous videos I was in front of a whiteboard. In this case, I’m writing on paper. Still not sure which way is better.

In this chapter:

  • Introduction.
  • Constant velocity in 1D.
  • Example of constant velocity.
  • Introduction to numerical calculations (1D constant velocity).
  • Constant acceleration in 1D.
  • Numerical calculations with constant acceleration (in 1D).
  • Solving the “cop chasing a speeder” problem.

Chapter 2: Forces and Motion

It’s tough to start in physics with forces. There are so many things to cover. This is a shorter chapter that looks at the fundamental ideas of force and motion.

  • Introduction to forces and motion. I really like this first video. It’s a conceptual look at the forces, the momentum principle and “Newton’s 2nd Law”. Guest appearances by Galileo, Aristotle, Newton.
  • Forces in 1D – falling objects.
  • Modeling the motion of a mass on a spring (and finding the model of a spring force). This one is long (but pretty nice).

Chapter 3: Vectors—2D and 3D Stuff.

The goal here is to expand kinematics into using vectors—but then you need to know about vectors.

  • Intro to vectors.
  • Kinematic equations with vectors.
  • Example of constant velocity and position update formula in 3D.
  • Intro to projectile motion.
  • Finding the range for projectile motion.
  • Numerical calculations for projectile motion.
  • Acceleration of a block on an inclined frictionless plane. This is an example of forces in 3D.
  • The physics of flying R2-D2. Using forces and air resistance.

Chapter 4: Calculated Forces

There are really two kinds of forces. There are forces that have an equation to determine the vector value (these are calculated forces). Then there are forces that don’t have an explicit equation (forces of constraint). This chapter just focuses on calculated forces.

  • Universal gravity.
  • Example of gravity—calculating the net force on the Apollo 13 spacecraft.
  • Introduction to visual objects in VPython. This is a setup for the next video.
  • Modeling the motion of an object near the Earth.
  • Modeling the Earth-moon system.
  • Mass on a spring (again) – but this time with visuals AND 3D motion.

Mapping the Electric Field and Stuff

This is really a note for Future Rhett. You’re welcome, Future Rhett. If anyone else wants to read this, please have fun.

OK, here is the problem. How do you describe the electric field around some region? Maybe that region is a dipole, or parallel plates, or some other random charge distribution?

Here are some options:

  • Equipotential lines. I assume you know what these are.
  • Electric field lines.
  • Electric field vector plot.

Let’s talk about these three. I don’t think I’m going to make example plots because I’m not sure what I want to do. Yes, I will probably do something in the near future.

Electric Field Vector Plot

Imagine you have a dipole (a positive and negative charge separated by some distance). The electric field vector can be calculated at any position (x,y,z). So for every location, there’s a vector.

But how do you display this visually? Well, you could just pick some points and plot the electric field as an arrow. Actually, I’ve done this before so I have a picture.

Image result for rhett allain dipole

Another option is to just plot the E field every cm (or some other set distance). Of course, this too has problems:

  • What about 3D?
  • What if the electric field gets too big and you have giant arrows?
  • What if the arrows are too small?
  • Can you do this on paper?

Still, I think this is probably the best option. Historically, no one ever did it this way because you pretty much need a computer to draw all those tiny arrows.

Equipotential Lines

I want to draw a picture here. OK, this is just a rough sketch.

Each of these lines represents a series of points at the same electric potential (with respect to infinity). They are fairly easy to draw and they give a good representation of the field—even though they aren’t the field. It’s just like getting the idea of a the shape of a mountain by looking at a topographical map. It’s the same thing.

How would you create these with a computer? That’s really what I want—that will make it useful for some strange charge distribution that you would have to calculate the field using a numerical calculation. Here’s what I would do:

  • Decide on the voltage line values. Do I want to do every volt or every 0.1 volts?
  • Pick a point. I don’t know where you would start—maybe near one of the charges?
  • Calculate the electric potential. I assume it’s not an even value of the potential lines. If you get 5.5 volts, you want to move down to 5 volts.
  • Now move in some direction. Check the voltage again. Did it go down? Keep moving that way. If it goes up, go the other way. If it didn’t change, turn 90 degrees.
  • Once you get to 5 volts, plot a point.
  • Move again, but find another point that is at 5 volts. Plot it.
  • Keep doing this until you get some set distance away from the starting point or you get back to the starting point.

This seems unnecessarily complicated. There’s got to be a better way. Figure it out Future Rhett.

Oh! What about this method?

  • Calculate the electric field every dx, dy point (so like on a cm grid). If the potential is a whole number 5, 4, 3, 2, 1 volts – plot a point.
  • I like this method better. More brute force.

Electric Field Lines

I feel like electric field lines are dumb. Oh sure, they give a good sketch of the electric field, but what do they mean? From my intro physics course (many years ago), I remember the following:

  • Field lines are always perpendicular to equipotential lines.
  • When field lines are closer together, the value of the electric field is greater.
  • The electric field vector is tangent to the electric field lines.

That’s about it. But how do you create these with a computer?

Here’s what I want to try:

  • Start at some point near a charge.
  • Calculate the value of the electric field vector.
  • Move in the direction of the electric field vector (some distance dr)
  • Again calculate E and make another move.
  • Keep doing this until either the electric field gets too big (in case you get near another charge) or the distance from the starting point gets over some distance.

I think this would work. I want to try it. That’s for you, Future Rhett.

Spring 2020 Class Update

Before I forget, I want to make some comments about my courses this semester.

Physics for Education Majors (PHYS 142)

I love this class. It’s one of my favorites. Just in case you aren’t familiar, it’s a course designed for elementary education majors (you could probably guess that from the title). We are using Next GEN Physics and Everyday Thinking (Next GEN PET). Oh—it’s awesome. Seriously, you should try this curriculum.

So, this semester things are going great so far. I normally teach this every semester, but last semester my section was cancelled. Apparently some particular college decided not to make this a required course (even though I made this course 12 years ago to satisfy their accreditation requirements). But by not teaching it last semester, I realize how much I enjoy it.

Oh sure, this semester it has much fewer students. However, I can have actual conversations with them as they work on the material. Also, the students have time to work on stuff. In the first unit they are building models of magnetism. It takes time to properly magnetize a nail. It’s slow process. I think more learning needs to take this slow process.

Special Topics: Numerical Calculations

Oh wait. This course was canceled. Damn.

Physical Science (PHSC 101)

I taught this class last semester. It went well enough.

This semester is a little different. Well, just one small difference. Instead of a large lecture class with desks and stuff, it’s a smaller room with tables. Here—take a look at this picture.

Surprisingly, this makes a HUGE difference. Now students can very easily have short discussion with other students. It makes a big difference. I like this room so far.

Intro Physics Lab 2 – Algebra-Based (PLAB 194)

I can’t just leave a lab alone. No, I have to change it every time I teach it. This semester, I want to focus more on building circuits. So far, they have only done the electric field mapping experiment. It seemed to be not too bad.

I don’t have anything else to see.

Intro Physics Lab 1 – Calc-Based (PLAB 223)

I picked this lab up at the last moment (because of the other canceled course)—so, I really didn’t get a chance to prepare ahead of time.

It’s a 3 hour lab (unlike the 2-hour algebra-based lab), so that’s kind of cool. My plan is to really focus on model building (with tons of python). It’s gonna be great. I hope.

Oh, even advanced students have problems making linear graphs.

That’s enough for now. I’ll keep you updated.

Just Enough Physics Chapter 1: Kinematics

Quick recap: I’m going through and redoing many of my physics videos. The idea is to put together a cohesive playlist that would work through the full physics course. I’m using the approach that skips over some of the more tedious topics—that’s why I’m using the “Just Enough Physics” title (yes, same as my ebook).

Well, I’ve got enough stuff for chapter 1. Here they are. Let me know if you think something should be added.

Introduction

Constant Velocity in 1D

Example with Constant Velocity

Introduction to Numerical Calculations for Constant Velocity

Constant Acceleration in 1D

Constant Acceleration with Numerical Calculations

Accelerating car catching a constant velocity car

Just Enough Physics Video Series

I think I need help. I’m not sure of the best way to proceed (or even to do it at all) with this new video project. Here is my idea:

  • Just Enough Physics – the video. Yes, a long time ago I put most of my physics explanations into a self-pub ebook on Amazon. I think it turned out OK. The book is in the KindleUnlimited program, so you might be able to get it for free – https://www.amazon.com/Just-Enough-Physics-Rhett-Allain-ebook/dp/B0052UKTDQ/ref=sr_1_1?keywords=just+enough+physics&qid=1578932997&sr=8-1
  • I’ve made a bunch of physics videos—but they aren’t well organized and they jump over to many different topics. I wanted to start over and make one series of videos that sort of go through the full intro (algebra-based) physics course.
  • In most of my previous physics videos, I used a white board with me in front of it. I think this works well, but I wanted to be able to make videos from home. With that, I decided to switch to a paper and pen method (with the camera just looking at the paper).
  • Also, I figured I would add a Patreon page. It would be nice to be able to work on this over the summer instead of teaching summer classes (which is always a financial gamble anyway). Oh, here is my Patreon page—https://www.patreon.com/justphysics

So, that’s the idea. Here you can check out what I have so far.

Now for the questions. Here’s where you can help.

  • Should I start a NEW YouTube channel for these videos or just include them in my current channel. I’ll be honest—I thought it would be good to start a new channel, but I need a bunch of subscribers before I can put ads on the videos. Yes, that’s silly.
  • I started off with an intro to each video and included a title animation. Forget that—too much work. I don’t think people REALLY care about that stuff.
  • What about Patreon? What kinds of things should I put there? Should I include access to a discord group?
  • Titles. How should I title each video? Chapter 1 section 1 kinematics? Constant velocity? I’m not sure. What about homework videos (example problems).
  • I’m aiming for each video to be about 10 minutes long. Is that a good time length?

Finally, here is my tentative outline for videos.

  1. Kinematics in 1 Dimension (including numerical calculations).
  2. Forces and the Momentum Principle in 1D.
  3. Vectors
  4. Calculated Forces: gravity, springs, real gravity.
  5. Falling objects air resistance.
  6. Forces of Constraint: normal force, friction, tension
  7. 2D Motion: projectile motion, circular motion.
  8. Orbits.
  9. Work-Energy Principle.

That’s just a start.

Top 10 Blog Posts from 2019

It’s always difficult to pick the BEST of stuff. This is especially true when it’s all your own stuff.

So, let’s just say these are 10 nice posts from 2019.

How Does the Mandalorian See Through Walls?

You know I love to write about stuff that gets me excited—and I’m super pumped up about The Mandalorian (just finished season 1). In one of the episodes, Mando sees through a wall with his sniper rifle. How would that work?

side by side photographs showing boy holding up sheet

No, it probably wouldn’t be with infrared.

Modeling the Water from a Spinning Sprinkler

You don’t really understand something unless you can model it. In this post, I use python to model the motion of water shooting from an inward pointing and spinning sprinkler (based on the Steve Mould and Destin video).

This gif pretty much sums it up.

Orbital Physics and the Death Star II at Endor

This is my favorite thing to do (which I also did in the Mandalorian post above)—take some scene from a movie and and then use that as an excuse to talk about physics. In this case, it’s all about geostationary orbits from Star Wars: Return of the Jedi.

Bonus: more python code in this post. Double bonus, I use data from ROTJ to estimate the length of a day on the planet moon of Endor.

All Measurements Are Really Just Distance—or Voltage

I was in lab when I realized that pretty much all of our measurements were actually measuring distance. Well, originally that was true. Now we can make measurements by measuring a voltage.

Here are some measurement devices—this wasn’t in the original post.

You Can’t Calculate the Work Done by Friction

This was a post I wrote after a discussion I had with Bruce Sherwood. He told me this story about how it’s easy to use the momentum principle with a sliding block (with friction), but you can’t use the work-energy principle.

We like to think friction is this simple thing—but it’s not. The above image is an illustration to show that the distance a friction force is applied is not the same as the distance the object moves.

Video Analysis of Captain America vs. Thanos

There is the perfect scene in Avengers: Endgame. It’s not only perfect because of what Captain America does—but it’s perfect for video analysis. So, in case you haven’t seen it, Cap takes Thor’s hammer and smacks Thanos hard.

Here is the frame corrected version after using Tracker Video Analysis.

No, momentum is not conserved. But that’s OK.

What are Maxwell’s Equations?

Yes, Maxwell’s Equations can be tough.

an equation

Here is my attempt to explain these equations in a simple way to describe the electric and magnetic fields.

Every Jedi Jump in Star Wars

OK, not every Star Wars movie. I didn’t have Episode IX to include at this time (I will have to wait for the digital version of the video). But the idea is to analyze ALL the jumps. Here they are.

There are too many jumps for me to do a complete video analysis. Instead, I just estimated the jump height and the jump time. From these two values, I can make a graph—if the vertical acceleration is constant then there should be a linear fit.

The best part is that most Jedi have a vertical acceleration LOWER than g (free fall acceleration on Earth). Yoda has a vertical acceleration HIGHER than g because he takes so many short jumps. I need to write a future post just looking at Yoda.

All the Hacks and Science from MacGyver Season 3

Maybe this is cheating since it’s really not just one post. This is a list of all my science explanations for MacGyver Season 3. Oh, just to be clear—I’m the Technical Consultant for the CBS show MacGyver (season 4 starts in February).

It’s a lot of work to help the writers come up with new science tricks for MacGyver, but it’s also super fun. I also really enjoy making these MacGyver at home videos.

I’m really looking forward to sharing more science for season 4.

Projectile Motion in Polar Coordinates

I’ve had this secondary blog for over a year now—and I really like it. It’s like the old days of blogging. I can write whatever the heck I want (example—the top five lightsaber fights in Star Wars). Also, I can go into super complicated physics stuff.

Here is an example from my upper-level classical mechanics course. Can you use polar coordinates for projectile motion? Yes you can—but it’s obviously not the best choice.

newplot (3).png

There’s python here too.

Best Graphs from 2019

It’s a tradition. At the end of the year, I like to post “top” stuff. Here are my best graphs. I’m only going to share graphs that I created with Plot.ly—although there are some other ones out there. So, maybe I should say “best plot.ly graphs of 2019”.

Oh, you haven’t used plot.y? That’s OK. Plotly, is an online graphing platform. It’s pretty nice. The thing I really like is that you can create some data in python (with Glowscript) and send it over to plotly for beautification.

One last thing. I don’t yet know how many “best” graphs I have—I haven’t looked yet. Also, these are in no particular order.

What ball is the best to catch with during free fall?

Here is the graph.

The graph is from this post—https://www.wired.com/story/the-right-ball-for-playing-catch-while-skydiving/. The idea was to consider what ball would be best to pass back and forth while skydiving.

Modeling a Moon Run

Here is the graph.

This is from my post looking at the physics of running on the moon. Actually, I really like this stuff. I built a model of a running human in which the final running speed depends on the foot contact time with the ground. I really just made the model so that I could use it for this moon running post.

Oh, bonus—here is my python code for the running model.

All the Jedi Force Jumps

Here is the graph.

If you look at all the jumps (in all the Star Wars movies) you can measure two things—jump height and jump time. Assuming there is a constant acceleration (not necessarily true) then there is a relationship between time and height.

a = \frac{2\Delta y}{(\Delta t)^2}

So, by plotting twice the height by time squared, the slope of the line would give the vertical acceleration. In the graph above, the green line is for an acceleration of 9.8 m/s^2 (the value on Earth) and the red line is the average for all the Jedi. Notice that Yoda has a greater acceleration. I think that’s cool.

Oh, bonus video. Here are all the Jedi jumps.

Course Reflections: Introductory Calc-Based Physics (PHYS 221)

The Course:

This is the calc-based physics course (the first semester). The students in the class are mostly:

  • Physics majors
  • Chemistry majors
  • Computer Science majors
  • Math majors

I don’t think there are any other students that take this. OK, I guess you could include pre-engineering—but technically they are still physics majors.

For the textbook, I use the super alpha awesome book Matter and Interactions (Wiley – Chabay and Sherwood). If you’ve read my stuff, you should know that I LOVE this book (and Bruce Sherwood and Ruth Chabay are both great people to talk to). Here is my previous review.

Just a few highlights of the curriculum.

  • Includes relativistic momentum and energy.
  • Focus on fundamental interactions and fundamental particles.
  • Ball and spring model of matter.
  • Three big principles: momentum, work-energy, angular momentum.
  • Explicit inclusion of numerical calculations.
  • I use Standards Based Grading with options for students to submit reassessment videos.
  • We often use multiple-choice questions in class with student response systems (clickers). Matter and Interactions has a nice set of questions to use.

Here is the course website.

The Good:

I always enjoy this course. The students are both diverse and great. They are at LEAST in Calc-I so that means they can probably do some algebra stuff. There are a good number of students that are in even more advanced math classes like Differential Equations and stuff. Oh, and it’s a great chance to get to know the new physics and chemistry majors.

The class isn’t too big (mine started around 30) so that it’s fairly easy to memorize names.

Maybe the best part of the class is watching student videos. OK, I really don’t like watching videos—it can get kind of boring. But I LOVE seeing students make terrible videos and then get better and start figuring things out. It’s awesome when students have never made a video and are afraid to do it, but then really get into it.

Students eventually figure out that I’m not just assessing their videos, but they are learning by making the videos.

One other thing I liked—I always like it: speed dating physics problem solving. Here is a twitter thread on speed dating (from another class).

Also, I did assign and collect homework. I didn’t really grade it (I gave them a score), but it’s like free points and maybe it helps them practice.

One last “good”. I put together this video tutorial on numerical calculations that looks at an object falling on the surface of the moon. I think it’s pretty good. Not sure how much the students used it though.

The Bad:

Yes, there was some bad stuff. Sometimes I felt like students were just sitting there. Even when I was doing interactive activities, they had this blank stare (it seemed). Maybe it was the class time (9:30 AM)—although that doesn’t seem too early. I really don’t know what the problem was. For the most part they were fine.

Another big problem—speed dating. Oh, I get it. Students don’t want to participate. They want to just sit there and take in the fire hose of learning (they think that works). But in the end, most of them seem to get some positive things out of the speed dating. But the room was not super great for this. It’s a standard lecture hall—so I didn’t really have places to put boards. I tried using very small boards, but it just wasn’t perfect.

One final problem—a good number of student just never seemed to fully grasp numerical calculations.

The Future:

Here are some ideas for the future.

  • Mounted white boards. If I have to be in that lecture hall, I want to find some ways to put boards somewhere around on the walls.
  • Plickers. I’m ditching the TurningPoint clickers. I’m tired of constant updates that bork the system. I get it—they want me to upgrade. Not upgrading again. Oh, also with Plickers it shows the student name over their head when they vote.
  • More in-class stuff. More group problem solving. More activities. More focus on numerical calculations.
  • I should show the students more of the awesome physics (like stuff from my blog). I don’t do this enough because I get so busy with getting through different topics—but I think the students really like these things. Who cares anyway, it’s the stuff that I love.