Today’s lab we are doing as a whole class in more of an interactive lecture demonstration format. The apparatus, procedure, and analysis are somewhat involved and I want to ensure that each student understands each step along the way. The purpose is to experimentally determine the moment of inertia of a solid disc and a ring. We will do this by first determining the angular acceleration of the system by graphing angular velocity vs. time. We will then determine the moment of inertia of the system by graphing applied torque vs. angular acceleration. We have to first determine the moment of the apparatus so we can subtract that from the moment of the disc and ring. There is a great opportunity for a side discussion of how the vertical intercept of the torque vs. angular acceleration graph is the torque due to friction in the bearing.
The data we collected in class looked good, but the experimental results show a moment of inertia ten times greater than what is calculated using the mass and geometry of the disc. We haven’t figured out what the problem is. We did realize that we weren’t accounting for the acceleration of the mass hanger and, therefore, the tension in the string is less than the force of gravity. However, I fixed that, and it had minimal impact on the results. If anyone sees a flaw in the experimental design, please let me know!
##setbacks ##paradigmlab ##expdesign ##rotationalmotion
We are exploring moment of inertia from several different perspectives. We’ve felt it experientially, derived equations mathematically, observed its effects, and will measure it experimentally. Today, I performed a simple demonstration of rolling two wheels of equal size and mass but different mass distribution down a slight incline. The wheels experience the same torque and yet clearly accelerate at different rates. It is a simple, but convincing demonstration of the effect of the moment of inertia of an object.
This morning I was at school at 5:30am to prepare for the school district’s Business Partnership Breakfast. I was proud to attend with my colleagues and three students from Huskie Robotics, FIRST Team 3061. We and our partnership with Navistar were being recognized. While addressing those in attendance, I focused on the mission of FIRST and how business partnerships go beyond the financial support that allows us to participate and be competitive and connect employees to students through mentoring. One of the students then shared her experience working with various mentors at Navistar. She did a fantastic job. We ended our presentation with a brief demonstration of last year’s robot. Since last year’s game involved frisbees, the distribute gave everyone in attendance a “business partnership” frisbee to take home!
##local ##makeitloud ##omgrobots
Today students practiced analyzing a system in rotational equilibrium. We had them hang two masses on the stick and calculate where a third mass should be placed such that the meter stick would be balanced. We then had students hang an object of unknown mass and calculate its mass. This was good practice for calculating torques. It was also good practice for their upcoming lab practicum. Throughout the activity, students discovered that the system would be more stable if the bracket at the center of the meter was oriented such that the screw was facing downward. Several pairs were surprised at the inaccuracy of their prediction until they realized that they didn’t account for the mass (and torque) of the mass hangers. One common thought among students was that the mass of the mass hangers didn’t matter since all objects were hung from similar mass hangers. I let them think about this for a few seconds until they realized that each mass hanger had a different length lever arm!
Despite panicking yesterday because I couldn’t find our Vernier instrumentation amplifiers (I’m still not sure I even have some), I was able to find a way to measure the small voltages produced by the Vernier Faraday’s Law – Moving Magnet lab. Instead of the more appropriate instrumentation amplifiers, which I’ve added to my equipment wish list for next year, I used differential voltage probes from old Vernier DIN-based current and voltage kits. The resolution wasn’t great, but with a strong enough magnet, it was sufficient for students to see how the induced emf changes as a magnet is dropped through several loops of wire.
I start class by asking students to share their pre-lab sketch of flux vs. time. I capture them all on the whiteboard and tell them to verify which one is correct by analyzing the data collected in the lab. What I love about this lab is the connection that students make that the area of the potential vs. time graph is the change in magnetic flux. This is a great lab to finish our study of electricity and magnetism.
##equipment ##paradigmlab ##setbacks ##magnetism
I like to introduce the concept of torque with “wimp sticks.” Wimp sticks have a handle which can be held by a student and a few hooks on which a mass can be hung. As the mass is moved farther from the handle, a greater torque must be applied by the student to keep the stick level. This difference is easily felt and demonstrates how the distance from the axis of rotation (the length of the lever arm) is proportional to the torque exerted by a constant force.
The part of the demonstration which further emphasizes the effect of the lever arm is when I give a second “wimp stick” to another student so he can have the same experience and feel the torque. (I choose both students carefully to avoid anyone who may feel embarrassed. This year, I picked two robotics students.) This second wimp stick has a much smaller diameter handle as is difficult to hold level without any additional mass and impossible to hold level with additional mass. We then as a class discuss if the student is as weak as he appears or if something else is having an effect. This discussion highlights that there are two torques which must be balance for the stick to remain level and that there are two different lever arms.
Something that I haven’t been good at is capturing insights during whiteboarding. Sometimes a student asks a really great question that results in a fantastic discussion. Sometimes I have an important question to pose that gets the discussion started. This year, I’m trying to capture this information in my daily reflections so I can consult it in future years. Today’s whiteboard involving a “rail gun” (Giancoli 5e, chapter 20, problem 17) is a great example of this. During my first class, we briefly discussed this problem and moved on. However, during my second class, a student asked about Lenz’s Law and the direction of the current. In this problem, a large current moves in a closed loop which is in an external magnetic field. The light bar experiences a force due to the current in the external magnetic field. The student questioned that the motion should result in an induced current in the opposite direction such that the generated magnetic field would oppose the change in flux. After some pondering, this led to a great discussion of back emf. At least next year, I’ll have this in my notes so all classes can benefit.
Today we started rotational motion in Honors Physics. We haven’t taught this topic for five year, and I’m thrilled its back in the curriculum. We’re trying to approach it in a modeling-centric manner. We are first exploring rotational kinematics and our “paradigm lab” was the Ladybug Revolution PhET simulation. This simulation was a great way for students to explore the quantities of angular position, velocity, and acceleration and compare with their linear/tangential counterparts.
Several students in AP Computer Science are struggling with the AP free response questions. In general, the logic is sound and the syntax is correct, but there is a lot of confusion about matching types. What I mean by matching types is making sure the type of the variable being assigned the value returned by a method is correct. Or, the type of the variable on which a method is invoked is correct. Or, the type of the variable being passed as a parameter is correct. Or, the type of the variable being compared to another variable are comparable. The transition from Python to Java’s strong typing is a challenge for some students.
This weekend, I thought of two representations that can assist a student crafting a solution to an AP free response question. The first is UML Class Diagrams, which is relevant to our current unit on object-oriented design. UML Class Diagrams capture everything important about a class in a single box and also shows the relationships between classes. The second representation, I just made up and there may be much more effective techniques. Today, I had students create a “type table”. One column is the variable name (including parameters, instance variables, this, and local variables). The other column is the type of the variable. I modeled how students can use this table, in conjunction with the UML Class Diagram, to check that their types are correct. Several students are trying this out tonight and we’ll see the results tomorrow.