# Advanced Rotational Dynamics for AP Physics - PowerPoint PPT Presentation

Advanced Rotational Dynamics for AP Physics

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Advanced Rotational Dynamics for AP Physics

## Advanced Rotational Dynamics for AP Physics

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##### Presentation Transcript

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 jet engine rotates about a fixed axis

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

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

17. electric motors power our elderly friends’ scooters

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

19. gears rotate about a fixed axis

20. 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)

21. 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

22. 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

23. 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

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

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

31. Look Ma, no hands

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

33. 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

34. 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

35. 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

36. linear and angular velocity and acceleration are proportional

37. rolling without slipping in our golden years

38. 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

39. 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

40. 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

41. 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

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

43. don’t try this at home

44. 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

45. 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

46. 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

47. 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