Inertia and Velocity • In the law of action we began with mass and acceleration • F = ma • This was generalized to use momentum: p = mv.
Moment of Momentum • To continue the analysis of rotational motion, we must also extend the idea of momentum. p r
Applying Torque • An external torque changes angular momentum. L L+rpsinq w w p
Spinning Mass • The moment of inertia is the analog of mass for rotational motion. • The analog for angular momentum would be: w
Angular Momentum Conserved • With no net external torque, angular momentum is constant. • The angular momentum of an isolated system is conserved
A system may have more than one rotating axis. The total angular momentum is the sum of separate vectors. Ltotal = Ls + Lw = Lw Internal Angular Momentum Lw w Ls = 0
Internal torques cancel out. Conservation requires that the sum stay constant. Ltotal = Ls + (-Lw) = Lw Ls = 2Lw Internal Movement Ls = 2 Lw -w -Lw
Conservation • With no external torque, angular momentum is constant. • DL/Dt= 0 • L = constant 4w w m r/2 r I = mr2 I = mr2/4 next