Learning objectives: Introduction to Rotational Dynamics beginning with the symbols used and rotational kinematic equations. We then stepped into Torque, defined. 

New Assignments: 

• Feel the Torque! This lab had students placing weights at various points on a meter stick and then holding the stick at predefined angles in order to calculate and feel the torque.
• Determination of Max Omega! This lab had students sitting on the “Sit and Spin” chair and simply measuring the maximum rotational velocity in RPM and Rad/sec. 

The opening discussion was focused on the symbols used in Rotational Dynamics (defined in chapters 10.1 and 10.2 of the OpenStax text book. Of special interest was the comparison between linear kinematic equations an rotational kinematic equations (illustrated in on page 425). On the second day, we delved into Torque as a topic (described in chapter 9.2 in the text) first introducing the concept of a force being applied at a distance away from an axis of rotation, then doing a mini-lab “Feel the Torque” and finally walking over to the autoshop.. so students could use a Torque wrench to tighten a lug nut on an old truck to a pre-defined Torque specification. (we also watched some youtube clips of wheel standing drag racers) 

Learning Objectives

New Assignments: 

• Feel the Moment (of Inertia). Students considered the acceleration of an ordinary hammer about three different axis. For each axis, students were to consider the hammer (the handle and the ‘head’) as the Sum of geometric objects, each with its own, Moment of Inertia. The students are to both draw the shapes individually, and showing what the equation of Moment of Inertia is for each, and then show how the total Moment of Inertia is the ‘sum of the parts’.
• Video: Johannes Kepler  While Clark was out, students were to watch and take notes this short (30 min.) documentary on Kepler’s life and accomplishments. Students should focus their attention on how his upbringing, how he survived, the role that Tycho Brahe played in his life and his theories of planetary motion. What are the three Laws of motion which he finally determined?
• Homework set: Problems 1, 5, 7, 8 on page 275 and problems 3, 7, 8, 11 on pages 460-461 of the on-line text book. 

This week introduced students to the concepts of Inertia for rotating systems. As in other systems, Inertia is the measurement of an objects ‘resistance to a change in velocity’. For objects travelling in a straight line, the measurement is simply the mass of the object measured in Kilograms. For a rotating system, the mass matters as well, but more importantly, the distribution of mass matters more. To begin the discussion, Clark considered a hammer, in which the head of the hammer (with significant mass) is rotated about a distant ‘axis of rotation’ and derived the fundamental equation for Moment of Inertia. From there we determined that for any distributed mass system, the total Inertia is simply ‘the ‘sum of the parts’. From here we considered various tables which present to us, the moments of Inertia for various shapes being rotated about various axis. 

Learning Objectives

New Assignments: 

• Model Moment of Inertia lab. This lab had students attempting to model the moment of inertia of a system consisting of an aluminum plate with three masses located asymetricaly on top (one of which was a force/accelerometer). They applied a known torque to the system, measured the subsequent rotational acceleration and from that, deduced what the ‘measured’ Moment of Inertia must be for the system. 
• rewrite: Why doesn’t the spinning wheel fall? Students were to ‘give back’ the lecture and demonstrations that Clark gave showing how ‘vector math’ predicts the solution of the wheel precessing about a new center-line. This Wikipedia page describes in detail, the torques which lead to precession.

This week introduced vectors as a way to describe various rotational dynamic properties such as angular momentum, torque and rotational velocity. The example given was the gyroscope effect of a spinning bike wheel not falling but instead preccess ing about an axis when released. Vector math is really the only way to consider this phenomena. 

Learning Objectives

New Assignments: 

• Podcast: The Science of Friction. Students were to take a page of notes, highlighting the factors that affect friction, how we measure it, etc.
• On-line Practice Ap Test. Students should see how well they do in this test and we’ll discuss next week. (note: The students need to log into the AP Classroom website to take the test. They MAY work together to discuss). 

This week began with continuing the discussion of the ‘inertia’ of a rotating system. The geometry of the mass matters more than the amount of mass (measured in Kgs).

As an exciting example of the Universe at Work.. we explored the world of Pulsars, Neutron Stars and Magnetars and how Conservation fo Angular Momentum is conserved and leads to objects  which spin at hundreds of times per second, but contain the mass of hundreds of Suns

With that in mind, the concept of Angular momentum and the conservation thereof, was introduced. For demonstration, Clark brought out a rotating platform/stool, and demonstrated how holding a spinning bike-wheel in different orientations resulted in the ‘system as a whole’ responding. Also, introduced, was the concept of using vectors to represent roational values (omega as the rotational velocity and L as the momentum vector.. L = I omega).

On Thursday, we stepped into the demonstration of the wheel being spun up and then being suspended by the end of axel rod. Clark then walked through the vector physics predicting the observed motion centered on the idea that ‘if you can see the direction of the forces/torque, you can also see the direction fo the change in velocity/omega). Students were tasked with taking notes during the lecture and then rewriting them such that they look like a college text book section on the matter.

• Introduction of Kinetic Energy of a rotating system and how we can use conservation of energy principals to rotating systems. Specifically we considered a disk rolling down a ramp and how the gravitational potential energy would be distributed between the rotational kinetic energy and the linear (translational) kinetic energy. 
• A special emphasis was placed on how to link linear motion (of a bucket falling) to rotational motion (of the pulley supporting the bucket). 

New Assignments: 

• Text book problems (page 461) 13, 15, 20, 22, 27, 32, 39.
• chpt 10_rotational dynamics and energy

This week students were introduced to concepts of conservation of energy in rotating systems. Just like in linear velocity systems, work is defined as force times distance, but in this case, we consider the force acting as a torque causing a system to rotate through an angular displacement. And how kinetic energy of a rotating system is analagous to kinetic energy in a linear system (with KE = 1/2 I Omega squared.). 

The main ‘new’ discussion was examining a problem in which a bucket suspended from a rope wrapped around a pully will descend by using the transformation from tangential velocity to rotational velocity to ‘tie’ the two components of the problem together.. Also discussed, was how we can use concepts of energy to determine the rotational velocity and linear velocity of a disk rolling down an incline plane.