Phy53 lecture dr. brown 5 october 2010
rotation
can independently treat translational and rotational parts of the motion
having done translational 'tis time to focus on rotational
key point -- rotation about pivot point -- all bits of mass rotate through same angle [rigid body]
torque \tau = r F_t --> sums -- external [internal cancel] -- Moment of inertia and
Newton's second law for rotation \tau = I \alpha
Calculating I for various symmetric objects I=\int{r dm}
Rod of mass, M and length, L : I = 1/12 M L^2
[about axis perpendicular to rod and through center of mass]
Disk of mass, M and radius, R : I = 1/2 M R^2 [about axis perpendicular to
parallel axis thm !
Total torque due to gravity
example: hoop w/pivot on edge of hoop
kinetic energy of rotation
K_{tot} = K of CoM + K about CoM
example: rolling disk down incline