1. Rotational Dynamics
The game plan…

2. A motivating problem
A cylinder of aluminum of mass g and radius m rolls down an incline of length 1.5 m and raised on one end by 0.15 m. How fast is the cylinder moving when it reaches the bottom and how many times has it rotated?

3. Important Analogies… Mass – Moment of Inertia Force - Torque
Momentum – Angular momentum
Kinetic Energy – Rotational Energy

4. Going from the translational world to the rotational world…
Radian measure

5. CoE still Applies!
Just add a new type of energy term:

6. What’s Rotational Energy
It’s a natural extension of the concept of kinetic energy
Angular velocity
Moment of inertia

7. What’s Moment of inertia…
It’s a natural extension of the concept of mass that accounts for how the matter in a body is distributed
The “how it’s distributed” part
The “mass part”

8. Try this…
A 2 m long bar of mass 5 kg and uniform density rotates from rest around the pivot point as shown. How fast is the tip of the bar moving as it hits the ground?
What is your strategy?
What additional information do you need?