2. 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)mv (½)Iω2
Work (constant F) Fd ?
CONNECTIONS: v = rω, atan= rα
aR = (v2/r) = ω2r , τ = rF , I = ∑(mr2)

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

4. 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)mv (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)

5. 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!)

6.  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!

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

8. Conservation of Angular Momentum
Example:
Diver