Rotational Dynamics The game plan…

A motivating problem A cylinder of aluminum of mass 147.89 g and radius 0.0784 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?

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

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

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

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

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”

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?