# Day 95: Circular Motion Force Diagram Assessment and Quantifying Radial Acceleration

Today the students took an assessment on drawing circular motion force diagrams.  Here is what I gave them:

You’ll see why tomorrow.

We also had a pre-lab discussion to develop and experiment that will allow us to quantify radial acceleration.  Through discussion, we arrived at looking at the relationship between radial acceleration and tangential velocity for a given radius.  Most kids decided that the radial acceleration would be affected by the angular velocity, the radius and the tangential velocity.  I asked if we could do an experiment where we varied the radius.  A few realized that it was not possible because varying the radius will also change the tangential velocity *if the angular velocity is not changed)… so simply moving out on the circular to change the radius also changes the tangential velocity.

Here is the experimental set-up being used:

That’s a Vernier WDSS zip-tied to a meter stick on our record players.  The tangential velocity will be measured using a Vernier Photo gate and One-Gate timing.  The students will do the experiment twice… a small radius and a larger one.  We did not get finished, so more data collection later.  Here is a screen shot on my own data:

# Day 94: A few more circular motion Force Diagram Demo’s

As I mentioned yesterday, I had a few more ways to recreate the circular motion force diagrams the students were drawing.  But first, here is the clip of the race track showing a banked corner vs. an unbanked corner.

Here is another of the situations the students drew a force diagram for:  (according my students, the drawing is a bit hard to interpret)

I know that it might be a bit of a stretch to have a vertical circle at constant velocity with a rope, but it simplified the FD for the students. Here we are re-creating it:

Here is the last one.

The discussion involved us getting to the point of recognizing that the tension force is not constant.  As part of the discussion, I asked the kids to sketch the tension force as a function of time graph. To check that, as well as the force diagram, we swung a Vernier WDSS in a vertical circle while capturing the video.  Really nice once the two are synched… you can see that when the sensor is at the top of the circle, the tension force is the smallest.  Unfortunately, I did not save the ones from class, but here is my practice:

General Physics:

Yep, I’m still teaching this course too.  There is not much exciting to post because much of what we are doing now, I have already written about with the Advanced class.

# Day 93: WB’ing AND Demonstrating Circular Force Diagrams –> That’s right, I said DEMONSTRATING

Today we started WB’ing the circular force diagram problems the students were given yesterday.  As part of the WB process, after we had agreed upon what the force diagram should look like AND some of the conceptual aspects of each problem, I demonstrated the problem.  Here is an example:

Many of my students have been on or seen a ‘spin and barf’ ride like this one.  Here is he demo I set up to show it to them:

Here is another one of the problems:

To demonstrate this one, I set up an old electric slot car race track.  I kept one end of the oval as a flat curve but made the other end banked.  I’ll add a video clip tomorrow, but you already know that the car leaves the track tangentially on the flat side.

Two others that I’ll share tomorrow.

# Day 92: Circular Force Diagrams and Motion Pillars take 2

Today we discussed the rotational kinematics assessment the kids took on Friday.  It continues to amaze me that even after a full semester with me, most of my students still reach for the equations….Here is  problem I gave them on the assessment

It is REALLY easy to solve with an angular velocity-time graph, but tougher and longer with the equations… sigh.

We also looked at sample tangential velocity problem I asked the students work on over the weekend.

That’s a picture of some wind turbines all my students have seen many, many times.   I asked them to determine the speed in miles/hour for the tip of the blade.  I provided them with the pdf of the design specs. The blade length is 134 ft and the operational rate is 14.4 rev/min….. the answer surprises most  138mi/hr.

After that we developed the concept of radial (or centripetal) acceleration.  I prefer radial because they are less likely to confuse it with centrifugal AND we hit a vertical circle we can discuss a tangential acceleration more easily.

General Physics:

We WB’ed the same set of motion pillars we used with the Advanced class.  I had 3 groups CYOP (create your own problem). One I used as an exit formative assessment, the other twoI will use as additional formative assessments.  We also just briefly started discussing how to draw force diagrams.  More on this tomorrow.

# Days 87-91: Still Trying to Catch up

These days cover the first week of our second semester.  I’m fortunate because I really do not have any new students, because I had them during the first semester.  So here was the week in review:

Monday — I allowed the students to see the problem set from the final exam.  Yep, that’s right, they saw the final exam after it was graded.  I feel assessments should be a learning opportunity and the final should be no different, the students SHOULD get to see the actual exam rather than a number on Infinite Campus.  We also had a brief introduction to our next unit, uniform circular motion.  We discussed the difference between rotating  and revolving.

Tuesday — We continued the discussion from the day before and built the concepts of  ‘angular motion key players’.  When we first started linear motion we talked about the key players; position, time interval, displacement, velocity and acceleration.  We developed all aspects (the conceptual, the graphical and the equations) essentially at the same time.

SIDEBAR: To review the concept of a radian I used a sweet little animated gif I found (possibly on Wikipedia?), here it is.

To accomplish this, I used a ‘mini merry-go-round of physics’ with a dry erase marker on it.  I also used a Vernier Photo gate and the Strobe setting.  I added a few calculated columns so I could display the angular position, and velocity graphs. Here is the set up:

Next time I use this, I am going to use a thin circular piece of wood to make a bigger platform and attach a series of evenly spaced (thin) metal strips to block the gate.  The values displayed will not be the actual angular velocity, but the graphs will be much cleaner.

The angular motion (kinematic) equations were built by the students using the displayed angular motion graphs and the linear motion equations.

We also had the pre-lab discussion for the first experiment, described next.

Wednesday and Thursday: The Tangential Velocity Experiment (shared a bunch of years ago by a former member of the Phox Share Group)

I replaced the marker (that represented a single point on the rotating platform) with my Einstein action figure.  The pre-lab discussion included Albert’s angular velocity and his instantaneous velocity— a linear quantity that is always tangent to the circular path.  We defined this as tangential velocity.  We talked about what might affect the tangential velocity.  Two factors surfaced: angular velocity and the radius of the circular path. So, two parts to the experiment:  Tangential Velocity as a function of Angular Velocity (with a constant radius) and Tangential Velocity as a function of radius (with a constant angular velocity).  Now, you and I know that we would not need to do both parts of the experiment, but the students do not.

Here is a picture of the experimental set-up:

We use two different photo gate files: Strobe (for angular velocities) and One Gate Timing (for tangential velocity). It’s hard to see, but there is a thin metal flag attached to the meter stick with a binder clip.  This is used to trip the gate.

I only have six  really well-functioning ‘mmgrop’ (mini merry go round of physics), so we broke the class in half.  On Wednesday, half gather data for the first part of the experiment while the other half did small group work on some rotational kinematic problems (solving both graphically and with the equations).  Thursday, we simply flip-flopped the groups.  The second data gathering group gathered data on the second part of the experiment.

Friday:  We started the period with a short one problem assessment on solving rotational kinematic problems, then WB’ed the results of the experiment.  I think most of you see that the slope of the linear tangential velocity as a function of the angular velocity graph has units that simplify to meters and represents the constant radius, while the linear tangential velocity as a function of the radius graph slope units simplify to the angular velocity.

General Physics:

With the start of the second semester, we begin dynamics with the general students.  We follow the same basic flow as we did with the Advanced classes.

Monday — The students also were allowed to look through their problem set from the final exam. After this, we gave them the a ‘Forces Diagnostic’ pre-test.  In both of my classes, the average score was about 10 (out of 30).

Tuesday — We discussed forces in a broad sense and then completed the Forces ILD to develop the concept of N3L.

Wednesday — We finished the N3L discussion and practiced identifying N3L pairs with balloon-o-copters.  Note to self– do not buy the cheap version, they work like ….

Thursday — We developed the concept of N1L using the Motion of a Cart with Two Tension forces.  As I wrote about with the Advanced class, this does an excellent job of clearly developing the differences in resulting motion when forces are balanced and when the forces are un-balanced.

Friday — We formalized N1L with several hands-on demos the students completed.

Whew.. all caught up again. Now if I can just stay caught up…..

# Days 82-86: I’m back and trying to catch up!

Ok, well, I’m back to trying to stay caught up with this 180blog attempt.  The first week in January was our first week back after the winter break AND the week before our semester finals.

SIDEBAR: I really, really, really dislike in a major way(OK, hate) our semester schedule…we have  two days of finals, a make-up day (no kids except those that need to make up an exam or something else) on Friday.  Then we turn around and start the next semester… it’s just not enough time. The Friday is a work day, but not a full one… all five of the instructors in that share my office had kids in to work on stuff and make-up stuff that the students had failed to make up earlier.

So here is how my final exams worked:

Monday — The 30 question multiple choice conceptual part.  Brand new questions covering our introductory unit, constant velocity, constant acceleration, projectiles, N1L&N3L, and N2L.  Why only 30 questions?  The test was given on a normal 53 minutes period AND they are really good, higher level questions… nothing just simply recall this fact.  They also completed one of the five problems from the problem set.  It was on using Logger Pro to create a graph, then interpret it.

Tuesday– The remaining problem set, one problem from each unit.

Wednesday — The lab practical.  The time frame was 80 minutes.  Essentially, the lab practical was a challenge lab.  It was based on an idea I saw in The Physics Teacher 2009 by David Jones called Time Trials — An AP Physics Challenge Lab.   it is an awesome activity and includes some kinematics as well as dynamics.

General Physics:

The general students did not complete a lab practical but had the other two components of the final exam, a conceptual part and a problem set.  Both parts of their final exam were given on the final exam day, 80 minute time block.

# Day 81: The Phox Share Groups ROCKS and WB the N2L Experiment

Before I explain what we did today in class, I want to once again say how awesome it is to have a local Physics/Physical Science Share group.  The Phox Valley Share Groups had another share session tonight, and it was awesome… a few science jokes, NGSS Evidence statements, holograms, rotary motion, a possible community outreach event, and a new take on an old favorite.  One of our members (Ryan Peterson @BrillionNerd) and a few of his students built a new and improved version of the Monkey and the Hunter that uses a Vernier DCU  in conjunction with a light sensor and laser pointer… TOTALLY AWESOME.

I’m sure most you know are already familiar with the WB discussion for the N2L experiment with the modified Atwood machine.  What I want to tell you about is one extra bit I have added.

We get to the point in the discussion where the slope unit of acceleration vs. net force graph are not really recognized (I know you know them, but my students don’t).  At this point I have not explained what is ‘inside a Newton’, we just use N.  So we have that acceleration is proportional to net force.  We also discuss ho acceleration is inversely proportional to the mass of the system. The slope units for the linear graph are also not recognized.  I explain that this is OK, because we want to join to the two parts of the experiment.  We end up with one relationship… acceleration is proportional to Net force/mass of the system.  To turn his into an equation, we need the proportionality constant (or slope) of a graph… acceleration vs. net force/mass of the system.  The students use a calculated column in Logger Pro to add this ‘new data’.  Here is what it looks like:

Notice the slope… 1.009m/s/s/(N/kg).  The slope value is 1.0 and the only way to get that is if what is on the y-axis is equal to what is on the x-axis…. so (m/s/s) = (N/kg) and after a bit of rearranging, N=(m/s/s)*kg… the definition of a Newton of force falls very nicely into our lap!

Now we can go back and explain the meaning of the slope of the other two linear graphs and formally write the equation for N2L that is so familiar to all of us.

General Physics:

We did a horizontally launched projectile ranking task.  To check it we used a little homemade device that I can’t recall where I saw.  Here is the ranking task:

Tomorrow I’ll include a picture of the device to check it.

# Day 80: N2L Data Gathering Set-up

As I explained yesterday, we are completing the data gathering for the Newton’s 2nd Law experiment using a modified Atwood Machine.  Here is a screen shot of some of the data gathered, and a movie showing the actual process.

As you can see, the process gives pretty nice data that is easy for the students to analyze, more importantly, understand where the acceleration is being gathered from.

General Physics:

Today was the WB discussion for the Video Analysis of a projectile experiment… nothing really that interesting to show because I talked about it here.

# Day 79: N2L Paradigm Experiment and VA of a Projectile

Well, the first day back after a long break is always tough.  Today was made a bit tougher because most students were thinking we would be under a 2 hour delay because of the weather… -31F with the windchill.  Some of the schools a bit north of us did go 2 hours late and some even cancelled… not use, it was only a Windchill Advisory, not a warning.  I’m actually glad we were not delayed.  We have to get started at so we might as well have a full day.  We actually have only about 7 days left in the semester, better get busy.

Today we had the pre-lab discussion for the N2L paradigm lab.  Like most modelers, I use the modified Atwood experiment, with a twist here and there.  My advanced classed usually do both parts  acceleration vs. mass of the system and acceleration vs. net force.  This year however, to save time, each group only did half of the experiment (odd cards did the first part, evens the second part).

SIDEBAR —> This was the first time in a whole bunch of years, that in one of my classes, net force as a factor affecting the acceleration DID NOT come up, so that class has everyone doing just the mass of the system experiment.

We start the discussion with two systems (the cart on the track, and the hanging mass as the other system).  We do force diagrams for both.  As we draw them, I ask about how the tension force in each diagrams compares.  My classes are pretty good at this point knowing that it is the same in both.  OK, so the Ft is the same in both diagrams, interesting.  I then ask about the acceleration.  It is split about 50-50, some say the acceleration of the phus is equal to the hanging mass, others say the phus is larger.  it only takes a few minutes of discussion for everyone to see that they have the same acceleration.  I have never had to check this with equipment (a motion detector), but next time I may just ask how we could prove it.  So, same tension force and same acceleration, so maybe we could treat the setup as one system rather than two.  This means the tension force becomes part of the system… this is nice because my kids agree it would be very difficult to measure the tension force while the cart is accelerating.

That’s all for now… tomorrow I’ll explain a bit more as the students will finish gathering data.

General Physics:

We started a new unit today with the General kids.  We are taking a look at projectile motion.  The students had a choice.. analyze the Basketball Shot movie that comes with Logger pro as one of the sample movies or shoot their own to analyze.  Either way, tomorrow we will WB the four graphs (x-t, y-t, vx-t, and vy-t).