phy 53 lecture dr. Brown 19 october 2010
cross product definition of torque --> definition of anglualr momentum
note: \vec{r} measured from a point [not axis]
Example:
baton rotating at angle about center point -- find angluar momentum
real issues with camera
note: \vec{L} does not equal I \vec{\omega}
L direction is precessing -- ther must be a torque
torque = \frac{2 \pi L_{\perp}}{T} = L_{\perp} \omega
relate example to balancing tires
Angular Momentum
orbit of earth about sun
sum of orbital angular momentum and spin anglualr momentum = total angular momentum
"orbit" of electron about hydrogen nucleus
L_orbital and L_spin => these are constant and can be used to "label" via principle quantum numbers
another example -- homework problem with hockey puck on frictionless table moving in circle...
note expressions for Kinetic energy
K = \frac{L^2}{2I} recall K = \frac{p^2}{2m} we used for collisions
work = change in kinetic energy
example: on turn table -- catch ball [collision] linear momemtum not conservered, nor is kinetic energy -- but angular momentum IS conserved
example: sweet spot for collision with rod -- center of percussion