Advanced Rotational Dynamics for AP Physics

1. Advanced Rotational Dynamicsfor AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia

2. Advanced Rotational Dynamicsfor AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia

3. Advanced Rotational Dynamicsfor AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia

4. Advanced Rotational Dynamicsfor AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia

5. Examples of rotation: Earth To find the direction of omega, apply the right hand rule as follows: With fingers curling in direction of rotation, the thumb gives direction of omega i.e. direction of earth’s omega is upward

6. rotation of the sky star trails centered on Polaris rotate once a day

7. rotation can be fun

8. sometimes the goal is rotational equilibrium • 1st condition for equilibrium: Fnet = 0 • 2nd condition for equilbrium: torque net = 0 • i.e., torque ccw = torque cw

9. rotational equilibrium again

10. sometimes the goal is large rotational velocity

11. M31 rotates once every few hundred million years

12. Katrina rotated

13. a generic kidney shaped object rotates about a fixed axis:a thing of beauty is a joy forever!

14. a turbine (driven by moving fluid) rotates about a fixed axis

15. a jet engine rotates about a fixed axis

17. steam driven power plant turbine:imagine this thing rotating at 60 hzgenerating your electricity

18. electric motors are backwards connected generators:they are still mechanical rotators about a fixed axis

19. electric motors power our elderly friends’ scooters

20. and nuclear subs also(when they are submerged)

21. gears rotate about a fixed axis

22. gear attached to an electric motor(sounds like a good idea to me)

23. nanotechology electric motor gear (the gear teeth are smaller than a red blood cell)rotating about a fixed axis, imaged with an electron microscope(end of examples of rotation)

24. Advanced Rotational Dynamicsfor AP Physics +Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia

25. Advanced Rotational Dynamicsfor AP Physics +Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia

26. Advanced Rotational Dynamicsfor AP Physics +Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia

27. Rotational Kinematics • Θ = angular position wrt arbitrary origin • Δθ = angular displacement (rad) • ω = Δθ / Δt = dθ / dt (rad/s) • α = Δ ω / Δt = d ω / dt = d2θ / dt2 (rad/s2) • s = r θ • v = r ω • a = r α

28. α = constant implies • Δθ = ω0t + ½ αt2 • ω = ω0 + α t • ω2 = ω02 + 2 αΔθ • Δθ = ½ (ω0 + ω) t • If α is variable, you need calculus

29. Intro Rotational Dynamics • Г = τ = r x F • I = Σ mi ri2 (collection of point masses) = ∫ r2 dm (continuous matter distribution) • I total = I 1 + I 2 + I 3 + … (composite object) • Fnet = ma becomes Гnet = τnet = I α

30. Advanced Rotational Dynamicsfor AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia

31. Advanced Rotational Dynamicsfor AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia

32. Advanced Rotational Dynamicsfor AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia

33. Earth revolves (translation of cm) and rotates about cm

34. Look Ma, no hands

35. combined translation and rotation Ktotal = Ktranslational + Krotational = Kof the cm + Karound the cm = ½ mv2 + ½ I ω2

36. Advanced Rotational Dynamicsfor AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia

37. Advanced Rotational Dynamicsfor AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia

38. Advanced Rotational Dynamicsfor AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia

39. linear and angular velocity and acceleration are proportional

40. rolling without slipping in our golden years

41. rolling without slipping • v = ω r (use with energy conservation) • atangential = α r (use with 2nd laws) • friction acts, but does no work • energy conserved as Wnc = 0

42. Advanced Rotational Dynamicsfor AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping (pure rolling) +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia

43. Advanced Rotational Dynamicsfor AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping (pure rolling) +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia

44. Advanced Rotational Dynamicsfor AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping (pure rolling) +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia

45. linear and angular velocities and accelerations are independent,i.e., he’s not getting very much bang (v) for his buck (ω)

46. don’t try this at home

47. rolling with slipping • v ≠ω r • atangential≠α r • apply Fnet = ma to find atangential of the cm • apply Гnet = Iα to find α around the cm • to compute t where pure rolling sets in, set a(t) = α(t) r, where a(t) and α(t) are solutions of force and torque equations

48. Advanced Rotational Dynamicsfor AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia

49. Advanced Rotational Dynamicsfor AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia

50. Advanced Rotational Dynamicsfor AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation +Rolling without slipping +Rolling with slipping +Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia