Physics 111: Elementary Mechanics – Lecture 11 Carsten Denker NJIT Physics Department Center for Solar–Terrestrial Research

November 14, 2006Center for Solar-Terrestrial Research Rolling Smooth rolling motion Rotation and translationReference frame

November 14, 2006Center for Solar-Terrestrial Research Kinetic Energy Stationary observer Parallel–axis theorem A rolling object has two types of kinetic energy: a rotational kinetic energy due to its rotation about its center of mass and a translational kinetic energy due to translation of its center of mass.

November 14, 2006Center for Solar-Terrestrial Research Forces Yo–Yo A net force acting on a rolling wheel speeds it up or slows it down and causes an acceleration. The acceleration tends to make the wheel slide. A static frictional force acts on the wheel to oppose that tendency.

November 14, 2006Center for Solar-Terrestrial Research Torque Definition of Torque Vector (cross) product (Right–hand rule, order does matter!) Revisit Chapter III!

November 14, 2006Center for Solar-Terrestrial Research Angular Momentum System of particles Angular counterpart of linear momentum! Definition [kg m 2 /s]

November 14, 2006Center for Solar-Terrestrial Research Newton’s 2 nd Law Single particle Linear form Single particle Angular form Proof The (vector) sum of all torques acting on a particle is equal to the time rate of change of angular momentum of that particle!

November 14, 2006Center for Solar-Terrestrial Research Conservation of Angular Momentum Angular momentum of a solid body about a fixed axis Law of conservation of angular momentum (Valid from microscopic to macroscopic scales!) If the net external torque acting on a system is zero, the angular momentum of the system remains constant, no matter what changes take place within the system