phy 53 lect			dr. brown			14 october 2010

Announcement: will drop 1 quiz for all

generalize rotations about any axis -- axis described via vector perpendicular to plane of rotation -- also must communicate orientation [cw or ccw] direction of rotation -->  right-hand rule [convention]

cross product [review and "know"]

note: we use right-handed coordinate system  \hat{x} X \hat{y} = \hat{z}

\vec{\tau} = \vec{r} X \vec{F}

more on definition of cross product of two vectors... using right hand rule

properties of cross products


Angular Momentum 

\vec{L} = \vec{r} X \vec{p} --> newton's 2nd law for ang. motion --> \vec{\tau} = \frac{d \vec{L}{dt}

...If total external torque acting on a system of particles equals zero, then the total angular momentum of the system is conserved!

... If \vec{\tau}_{ext} = o , then \vec{L}_{tot} is a constant vector

Conservation of Angular Momentum!

demos  ...

MRI's explained ...precession

demo'd with bicycle wheel

calculated example with wheel as spinning top

must know how to do this!  [there exists a cleaner calc based method]