Translation-Rotation Analogues & Connections Displacement x θ Velocity v ω Acceleration a α Force (Torque) F τ Mass (moment of inertia) m I Newton’s 2nd Law ∑F = ma ∑τ = Iα Kinetic Energy (KE) (½)mv2 (½)Iω2 Work (constant F) Fd ? CONNECTIONS: v = rω, atan= rα aR = (v2/r) = ω2r , τ = rF , I = ∑(mr2)

Work Done by a Constant Torque Torque: τ =Fr Work: W = F = Frτ = ττ

Translation-Rotation Analogues & Connections Displacement x θ Velocity v ω Acceleration a α Force (Torque) F τ Mass (moment of inertia) m I Newton’s 2nd Law ∑F = ma ∑τ = Iα Kinetic Energy (KE) (½)mv2 (½)Iω2 Work (constant F,τ) Fd τθ Momentum mv ? CONNECTIONS: v = rω, atan= rα aR = (v2/r) = ω2r , τ = rF , I = ∑(mr2)

Section 8-8: Angular Momentum Define: Angular Momentum of rotating body (moment of inertia I, angular velocity ω): L  Iω (kg m2/s) Recall, general Newton’s 2nd Law: ∑F = (p/t) (= ma)  if ∑F = 0, (p/t) = 0 & p = constant Momentum is conserved if the total force = 0 (collisions!)

 if ∑τ = 0, (L/t) = 0 & L = constant Angular Momentum L  Iω Similar to momentum case, can show, rotational version of Newton’s 2nd Law: ∑τ = (L/t) (= Iα)  if ∑τ = 0, (L/t) = 0 & L = constant Angular Momentum is conserved if total torque = 0 Example: t = 0, angular velocity ω0 time t, angular velocity ω L = L0 or Iω = I0ω0 Change moment of inertia from I0 to I by changing the body’s shape!

Conservation of Angular Momentum Example: Ice skater: L  Iω. But I =∑(mr2)  Iω = I0ω0

Conservation of Angular Momentum Example: Diver