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]