1. 1/16/20078.01L IAP 2007  Last Lecture  Everything you need to know about dynamics of rotation  Today  Pendulums and Kinetic Energy of rotation  Important Concepts  Equations for angular motion are mostly identical to those for linear motion with the names of the variables changed.  Kinetic energy of rotation adds a new term to the same energy equation, it does not add a new equation.  Kinetic energy can be simply written as a linear term and a rotational term

2. 1/16/20078.01L IAP 2007 Important Reminders  Note that tutors have both assigned and open sessions this week. See web for schedule  Mastering Physics due tomorrow at 10pm.  Experiment in class on Thursday.  Note that if you do NOT do the necessary calculations in advance, there is a good chance that you will NOT be able to finish the experiment in time.  Problems-solving in recitation this Friday.  Pset due this Friday at 4:30pm.

3. 1/16/20078.01L IAP 2007 Right-Hand-Rule Review (by request)  Except for the gyroscope, all 8.01L problems can be solved without using R-H-R, use CW/CCW instead.  However, many problems in 8.02 require R-H-R  The vector for any angular quantity ( , , , , J) points along the axis with the direction given by:  Fingers curl in direction of , , , , J, thumb points in the direction of the vector  Cross-product Right-Hand-Rule: Fingers point along vector A, curl fingers to point along vector B, thumb points in direction C.

4. 1/16/20078.01L IAP 2007 Pendulums  Simple pendulum: Small mass at the end of a string  Period is where l is the length from the pivot to the center of the object.  Physical pendulum: More complex object rotating about any pivot  Period is where l is the distance from the pivot to the center of mass of the object, M is the total mass, and I is the moment of inertia around the pivot.

5. 1/16/20078.01L IAP 2007 Parallel Axis Theorum  Very simple way to find moment of inertia for a large number of strange axis locations.  I 1 = I c.m. + Md 2 where M is the total mass. d c.m. Axis 1

6. 1/16/20078.01L IAP 2007 Kinetic Energy with Rotation  Adds a new term not a new equation!  Rotation around any fixed pivot:  Moving and rotating:

7. 1/16/20078.01L IAP 2007 Everything you need to know for Linear & Rotational Dynamics    This is true for any fixed axis and for an axis through the center of mass, even if the object moves or accelerates.  Rolling without slipping:  Friction does NOT do work!  Rolling with slipping:  Friction does work, usually negative.  Rarely solvable without using force and torque equations!