Special Topic for Sabio Academy Students: Rotational Motion

These lectures are for the AP Physics B students to study the concept of Rotational Motion.  The Rotational Motion is not covered in the AP thus most AP Physics courses do not teach this subject.  However, the SAT Subject Test covers it.  The SAT Subject Test never gets into heavy computation or problem solving.  Thus studying these concepts in this summary form would allow you to get a few more points without much added effort.

These lectures are delivered in two parts.  Part 1 is the concepts where the terms and concepts are explained.  Part 2 is the practice where typical SAT Subject Test problems are solved and explained.

Physics of Rotation  Part 1 Concepts

First, let's understand the cast of characters that appear in the world of all these "Angular This"™ and Angular That"®

Introduction to the physics of rotation.

Angular displacement.  What is it?   

 And how do you convert between linear and angular displacements?

Angular Velocity.  What is it?  And how to convert between linear and angular velocities?   

You can also calculate angular velocity from angular displacement.

Angular Acceleration.  What is it? 

You can express the Centripetal Acceleration in terms of ω and r as follows.

There is a relationship between ω and the frequency.   

As it turns out, ω can be found in several ways.  Here they are. 

All these similarities and analogies with the linear world is compared and summarized here.   

Let's observe a rolling wheel.  The physics of it is rather interesting.

Now, we will examine closer the strange world of angular mass (moments of inertia), angular force (torgue), angular momentum and angular energy.

What exactly is a torque?     Is that all?  Just multiply force with distance? 

Well, there is one minor detail.    Now, you know torque completely. 

Now, we enter the wonderful world of Moment of Inertia.   

The moment of Inertia can be derived for a simple case like this one. 

Even if the mass is the same, the moment of inertia varies depending on how that mass was shaped. 

The moment of inertia was the most complex part.  Now, angular kinetic energy is exactly what you expect it to be.     The most popular way the SAT tests your understanding of Rotational Kinetic Energy looks like this. 

The last angular quantity is the momentum.  It is also straight forward now that you know the angular mass (moment of inertia) 

The most striking aspect of all this angular business is the Conservation of Angular Momentum.

Physics of Rotation  Part 2 Solved Problems