Oh, GoPro! Frame of Reference Issues.

GoProGoPro videos are an exciting way to capture motion events. Since I can’t help thinking about physics, I wondered if it would be possible to analyze the motion to determine speed and acceleration. I wanted to figure it out so that every time I did something fun and recorded it, I would be able to go back and see how fast I was going or how great my acceleration was.

I found that using these videos to analyze motion using LoggerPro creates some problems.

Traditionally, the videos we have used for analysis are recorded with a stationary camera and a moving object. The fixed background provides a reference frame through which an object moves. But with the GoPro, the camera seems stationary while the world flies past.

I took a GoPro video while riding my bike on a sunny day. In this way, I had a second measure for the bike speed. In the shadow, you can see the wheel going around. So I decided to compare the speed of the bike using data from the shadow and data from the video to see if using video analysis was reliable.

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Click Here To View the Video

Speed Calculation – Method 1 – Circumference and Time

The GoPro records 30 frames per second. If you watch the tire stem as it travels around, you discover that it takes 22 frames or 0.733 seconds to complete one rotation. During this time the bike travels forward one circumference.


The diameter of the bike wheel is 65 cm and circumference of 2.042 m.

Screen Shot 2014-11-10 at 4.13.51 PM

This yields a speed of 2.79 m/s using the circumference and time for one rotation.

Speed Calculation – Method 2 – Video Analysis

As with all video analysis, some object of known size is used to determine the scale. A meter-stick serves as a good measure as long as it is placed the same distance from the camera as the moving object. If it is not, errors arise. (See previous post). The camera and the reference meter-stick remain the same distance apart through out the video.

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The GoPro video is different. All objects in the field move relative to the camera. To overcome this aspect of the video, I chose to do the analysis within a small area directly in front of the camera. The GoPro has a fixed focus of 4 ft. In the bike video analyzed here, the area directly in front of the bike wheel was chosen. At the start of the video I found a feature of known length (85 cm) and was perpendicular to path of motion.

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I chose a spot in the road that was moving directly toward me (that I was moving directly toward?) and recorded its position in 8 frames. The data looks fairly straight on the graph, so the slope of the line should represent speed.

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This graph shows the slope of the line if all 8 points are included. The slope, and therefore the speed is 2.451 m/s. That result is a little disappointing. Recall that the speed from method 1 was 2.785 m/s.

After some consideration, I decided that part of the problem was that the farther away from the camera the spot in the road was, the less correct the reference distance was. If that were true, the more points included, the less correct the results would be.

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If I only included the last 4 points in the analysis, the speed was determined to be 2.698 m/s. That was somewhat better!

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If only the last 3 points are used the speed is determined to be 2.791 m/s.

So, the agreement between the two methods improves as fewer points are used, perhaps because the reference distance is more true for these later points (when the spot is the road was nearer to the bike).

I would not usually be in favor of ignoring some data points, but in this case there is a clear reason for doing so. This would be a good conversation to have with students, when would such a decision be legitimate?

I hope this helps you think about some of the issues associated with using video analysis with GoPro videos. This situation was very contrived. The road at least was always a fixed distance from the camera. I imagine that if you jumped off a cliff, nothing would remain constant and the analysis would be even more complex. It does, however, provide another opportunity to talk with students about frame of reference.

Always, your helpful comments are welcome.

Video Analysis – Tips for Making Good Movies

Video analysis provides a great way for students to understand all kinds of motion that is just too darn hard to measure any other way.

In an ecology class in 1975, my lab group and I ran around a flower field, following a bee, sticking a flag in the ground every time the bee landed, timing how long the bee stayed on the flower, shouting out numbers for the recorders to write down, and returning later to measure the positions of the flags. We used slide rules and the “sum of least squares” to see if there was any correlation between the time the bee spent on the flower (as an indicator of food quantity) and the angle and distance the bee flew to the next flower. We thought perhaps that a bee would try to stay in the area (sharper angle, short distance) when it had found a good food source. After a week of work we found the dreaded “no correlation”. Imagine how different that activity would look today. We would place a video camera over the flower field and clickity click click, collect some data. Open some graphing software and the analysis would be done in minutes.

Video is so easy to collect these days that students can record any kind of motion they want and apply newly learned physics rules to understand it. One of my students video-taped herself jumping a barrier on her horse. She discovered that she moved in such a way that she always kept herself over the center of mass of the horse. We had a great discussion about why this might be so.

Sometimes my students get bad results. I have learned a few tricks that increase the likelihood that they will get good data.

We used Vernier’s Logger Pro. It has a great tutorial. That is how I learned how to do video analysis and I use the tutorial to teach my students. Try it, you won’t be sorry.

In Logger Pro choose, File -> Open. Among the folders that contain the science experiments, you will find a folder called Tutorials.


Video Analysis

Select 12 Video Analysis.cmbl. Follow the instructions and don’t skip anything. And tell you students not to skip anything.

The cursor that is used to locate the objects in each video frame is cross-hairs. Students usually think it best to put the center of the cursor on the center of the object. But the cursor obscures the view of the object somewhat and the center of the object is a judgement call. I tell them instead to place the top of the cursor on the top of the object.

Place the top of the cursor on the top of the ball.

Place the top of the cursor on the top of the ball.

Students should enlarge the movie screen as much as possible when locating the object in each frame. Click the movie, grab a corner and stretch the movie. After the locations have been determined, the movie can be made smaller again.

Students need to use an some object in the video of known size to set the scale. In the sample basketball video, there is a two-meter stick on the floor. If the students themselves are in the video, their height can be used.

It is important to place the meterstick the same distance away for the camera as the action. In the sample video, notice that the meterstick and the ball are the same distance.

Some of  my students were having trouble with data, so I decided to see how much difference it would really make if the meterstick were too far or too close. In picture from the video shown here, you can see there are three metersticks. The center one is in the correct position, the others are too close or too far. My hidden associate, Ian, tosses a ball. Click on the link below the picture to watch the video.

Three metersticks placed at various distances from the camera.

Three metersticks placed at various distances from the camera.

Click Here to View the Video

Since we know the acceleration due to gravity is 9.80 m/s/s, we have a way to check our accuracy. The actual analysis screen shots are included at the end of the post. Here is a summary of the results of the analysis:


As you can see, the position of the reference meterstick makes quite a difference. It is an important consideration.

You might be wondering why the data from the correctly positioned meterstick didn’t give us a value for the vertical acceleration that was closer it -9.80 m/s/s. When I used the basketball video from the tutorial I got a value of -9.607 m/s/s. The results were better because the video was better.

The video I used was shot under low light levels. The camera collects light for a longer period of time for each frame when light levels are low and as a result, the image is blurred. This makes it difficult to get really accurate positions. The object in my video is small and hard to see. The basketball is much larger and easier. Sometimes we paint a white or black spot on the object to make it easier to see.

So, here is my list of things to do in order to get good video analysis results:

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I usually have my students arrange the video, data table, and graphs on the screen and take a screen shot. These files are uploaded to a Google folder that is shared with me. This is there way of “turning in their lab” without wasteful printing. If you want more information about how to do this, see the previous posts on video analysis and the NSTA STEM14 tab for information on using Google Drive.

As always, you helpful comments are welcome.

Here are the images of the data analysis in case you would like to see them. Click on the images to see them enlarged.

Acceleration with meterstick in correct position.

Acceleration with meterstick in correct position.

Acceleration with meterstick too far away.

Acceleration with meterstick too far away.

Acceleration with meterstick too close.

Acceleration with meterstick too close.

Horizontal Velocity with meterstick placed correctly.

Horizontal Velocity with meterstick placed correctly.

Horizontal Velocity with meterstick too far.

Horizontal Velocity with meterstick too far.

Horizontal Velocity with meterstick to close.

Horizontal Velocity with meterstick to close.

Measuring Static Friction – an Extreme Example

Once you study physics, you are forever its willing prisoner. One of my favorite and most used tags for posts is Can’t Help Thinking About Physics. Here we go again.


Static Friction

While sitting on a leather sofa, visiting with my daughter, we noticed that her phone (in its rubbery case) wasn’t sliding down the cushion. She placed the phone at a steeper and steeper angle until finally it did slide.

We use this method, tilting a surface until an object slides, to measure the coefficient of static friction in our introductory physics class. I had never seen anything tilt this far before sliding. So, of course, I snapped a couple pictures so we could calculate mu.

Angle Measurement

I tried to hold the camera as nearly horizontal as possible, using the arm of the sofa as reference. I used the “selection cursor” of the computer’s own preview software to measure rise and run of the slope. It gave me the pixel dimensions (51×116) of the selected area and using the tangent function, I calculated the angle.

tan calc

Because I chose the angle where the phone JUST began to slide, the component of the gravitational force parallel to the surface (Fp) is equal to the force of friction (Ff). At any angle less than this, Ff would be larger than Fp and the phone would not slide. At any angle greater than this, Fp is greater than Ff and the phone would slide and accelerate. As Goldilocks would say, this angle is “just right.”

If you haven’t seen the math, here is a diagram. I usually have my students work through the calculation of Fp, Ff, and Fn. They just have to realize that IN THIS CASE, Fp is equal to Ff. They are usually amazed that mu = tan theta until they have had some time to think it through.

scans 001

I have attached a copy of a student lab in case anyone wants to use it. It certainly falls into the category of “Cheap Labs” but is still very rich. In the student lab, they first calculate the coefficients (starting and sliding) for a physics book. I guess you really do need physics books. They also calculate mu for their shoe. It is amazing the range of values that shoes yield.


Still, this phone with a static friction mu of 2.27 really surprised me. I was thinking that maybe adhesion was playing a roll. While friction prevents surfaces from sliding past each other, adhesion can be investigated by determining how much force it takes to pull surfaces apart. We did a crude test by placing the case on the floor and trying to pick it up with the cushion. It did not stick so I guess adhesion was a small factor and mu really is very high.

I think that a modified version of this activity would make a pretty good science fair project for elementary school. You wouldn’t really have to do all the math, just recognize that relative friction can be measured by how high you have to raise the end of an incline to get an object to slide. Perhaps various shoes could be measured, or toy vehicles, or flooring types.

As always, your helpful comments are welcome!

Dividing Up the Budget

It’s that time of year again. Departments get a budget and order supplies for next year. At the school I am working at, the budget is for the entire department. So I decided to create a spreadsheet that would allow each teacher in the department to get an idea of how much they could spend.

We started out by acknowledging that some courses cost more to teach than others. It’s not that everyone couldn’t spend money if they wanted to, but traditionally chemistry has more consumables that physics. So we sat down as a department and decided how much of the budget should be allocated to each course. We assigned the courses a “factor” between 1 and 7 based on their “costliness”.

After that, it was easy to build a sheet that counted sections and “factors” and divided the budget. There are a couple little tricks build into this one. For instance, no section gets less that $100 no matter how many sections of the other, more expensive courses there are.

budget SS pic

The numbers don’t add up to the budget exactly due to some rounding.

When each teacher gets their schedule, they put in the number of sections of each course they are to teach and it returns their personal spending amount.

Of course, no one is required to spend all their money and some teachers pool their resources. But it is a good starting point and a way to start a conversation about budget issues.

Here is a link to the actual spread sheet. Try it out and modify it in any way you like. It has worked well for us.

Budget Spreadsheet

Factors Affecting Resistance Lab – Free Lesson Plan


If you are teaching about electricity and you don’t have any lesson plans for today or you have to be absent sometime soon and don’t have plans for the sub, this post is for you!

We study electricity using CASTLE, a program for teaching conceptually about electric circuits. It is well supported by research that students who experience this program are more likely to give up commonly held misconceptions about circuits. My students are able to learn the “formulas” in a very short time after our work with CASTLE. I am, as you know, a big fan.

The concept of resistance is clearly demonstrated in CASTLE using carbon resistors and bulbs with different amounts of resistance. But I like to add this lab to our post-CASTLE unit because resistance is so interesting and measurable.

The format of the lab is also one I like to use. If every student is doing the same thing, you need a complete “class set” of materials. But if you set the lab up in stations, the students move around and you can take advantage of objects that you may only have one of. This lab started out with just four stations and I used it to illustrate the factors that affect the resistance of a wire (length, diameter, temperature, and material).

But it was easy to add stations as I learned something interesting or acquired a unique piece of material. When the electrician came to my room to fix the thermostat, he replaced the thermistor just in case it was bad.


It was not defective, so now I have the exact device that measures the temperature of my classroom for the students to play with in lab. I went to the hardware store and picked up interesting switches and dimmers that rely on resistance and made them into stations.

So here is what you will find in the folder if you follow the link:

1. A copy of the student lab paper.
2. A copy of the instruction sheet that I use at each station (and a necessary table for station 9)
3. A short video of each station that can be used with the student material to collect data.

I like having the videos, because then if a student misses lab, they can see the videos and still collect data from them and answer the questions. You can use the videos in that way for your whole class, or better yet, use them as a guide to set up the actual lab in class.

Click on the links below:

Student Lab Sheet

Station 1 – Length of the Wire           Instructions     Video
Station 2 – Diameter of the Wire        Instructions     Video
Station 3 – Type of Material               Instructions     Video
Station 4 – Temperature                      Instructions     Video
Station 5 – Color Code                       Instructions     Video
Station 6 – Variable Resistors             Instructions     Video
Station 7 – Photocells                         Instructions     Video
Station 8 – Thermistors                       Instructions     Video
Station 9 – Resistivity                         Instructions     Table      Video

I would really love to hear from anyone who uses the material. Let me know if it is useful, how you use it, how I could be more helpful.

Sources of Continuous Voltage – Demonstration Videos

I recently posted some videos of the activities in the CASTLE curriculum program for teaching students about electric circuits.

As a supplement to those activities I do a demonstration showing ways that a continuous voltage (and therefore current) can be maintained.

I have posted 6 short videos that show these demonstrations. Try them yourself with your students! Ask the students what they know about their utilities; gas, water, electricity. Some have no idea where these things come from, where the power plant and water towers are. They will be interested!

Continuous Voltage Demos
Electromagnetic Induction Part 1
Electromagnetic Induction Part 2
Chemical Cell
Solar Cell
Piezoelectric Cell 


If you have read my posts before, you know that I like the CASTLE program for teaching about electric circuits. The students work their way through several sections of material that address common misconceptions held by high school students about electricity. The program asks them to rebuild their mental model based on the evidence they see as they build circuits. An important part of this learning is the inclusion of a 25,000 microfarad capacitor in some circuits.

Students work in pairs, often consulting the other pair of students at their table. The teacher leads the class in model building at intervals. Students learn to color code circuits to help understand what is happening.

I have created some videos of the actual lab activities associated with the first 6 sections. I did so for several reasons:
1. To help students who are absent catch up.
2. To help teachers who are using CASTLE for the first time see what to expect and check their results.
3. To allow students who have completed lab work to review what happened while they are studying or completing homework.

The videos are not intended to replace the actual lab work done by students in class. Though, if a person were studying physics and had no access to lab equipment, the videos could be used to help them work through the CASTLE materials.

The videos have relatively low production quality (I have no crew) but hopefully good usefulness. My own students report that they use them to keep up when they are absent (25%), review (75%), check to see if they “did it right” (50%), work ahead (5%).

Let me know if you think they are useful! Your helpful comments are always welcome.

Section One

Investigation One Part 1
Investigation One Part 2
Investigation Two Part 1
Investigation Two Part 2
Investigation Three Activity 1.8
Investigation Three Activity 1.9 Large Bulb
Investigation Three Activity 1.9 Small Bulb
Investigation Three Activity 1.10

Section Two

Activity 2.1
Activity 2.2
Activity 2.5
Activity 2.8
Activity 2.9
Activity 2.12
Section Three

Activity 3.5 step1 (0.025 farad capacitor)
Activity 3.5 step3 (0.025 farad capacitor)
Activity 3.5 step5  (0.100 farad capacitor)
Activity 3.7
Activity 3.13 with Old Used Batteries

Section Four

Section 4.1

Section Five

Activity 5.1
Activity 5.2
Activity 5.3
Activity 5.5
Activity 5.7
Activity 5.10
Activity 5.12
Activity 5.13
Activity 5.15

Section Six

Close Up Photo of Digital Multimeter
How to Use a Voltmeter
How to Use an Ammeter
Activity 6.4a
Activity 6.4b
Activity 6.4cActivity 6.5
Activity 6.6 part1
Activity 6.6 part2
Activity 6.7 a-c
Activity 6.7 d-f
Activity 6.9
Activity 6.10
Activity 6.12
Activity 6.16
Activity 6.19
Activity 6.20 c