1. Torque, Equilibrium, & Dynamics Torque Dynamics Rotational Inertia Angular Acceleration Equilibrium Rotational Energy Angular Momentum

2. Torque, r F rFsin( )= r F = r F

3. Torque, r F r F F

4. Torque, r F r F r

5. Torque x y Fx Fy

6. i x i = j x j = k x k = 0 i x j = k j x k = i x y z x y z k x i = j j x i = -k k x j = -i i x k = -j A x B= (A x i + A y j +A z k) x (B x i + B y j +B z k) = (A y B z - A z B y ) i + (A z B x - A x B z ) j+ (A x B y - A y B x ) k ++++ - --

7. Angular momentum L = mvrsin = mv r L = mrv = mr 2 = I =I =I / t = L / t = L / t r v

8. Conservation of Angular Momentum If = 0 then L is constant. Usually, L=m v r Or L = I

9. r1=4.0 m & v1=3.0 m/s v2=? When r2=1.5 m

13. = L / t