1. Outline Kinetics – Linear & External Forces in human motion Mechanical work, power, & energy Impulse-momentum – Angular, External and Internal Torques in human motion Mechanical work, power, & energy Impulse-momentum

2. Outline Muscle/Joint Mechanical work, power, & energy Definitions Examples Impulse-momentum Definition Examples

3. Outline Muscle/Joint Mechanical work, power, & energy Definitions Examples Impulse-momentum Definition Examples

4. Net muscle mechanical work at a joint (U m ) Product of moment and angular displacement Example U mus = M mus * ∆  Units: Joules M mus ∆∆ Elbow

5. Positive net muscle work: M mus & ∆  in same direction U mus = M mus ∆  Muscles do work on the forearm M mus ∆∆ Elbow FwFw Example

6. U mus = M mus ∆  Muscles absorb mechanical energy M mus ∆∆ Elbow FwFw Negative net muscle work: M mus & ∆  in opposite directions Example

7. Net muscle mechanical power (P mus ) Product of moment and angular velocity P mus = U mus / ∆t = M mus *  M mus &  in same direction (same sign) P mus > 0 (power output) M mus &  in opposite directions (opposite signs) P mus < 0 (power absorption) M mus  Elbow FwFw

8. P m = M m * 

9. Area under power vs. time is work.

10. Jump: no countermovement Mechanical power & work Always positive Mechanical work Hip > Knee >Ankle

11. Compared to a jump without a countermovement, will the mechanical power in a countermovment jump a)the same? b)different?

12. Time (s) WALK 1.25 m/s 0 700 F g,y (N) 0 0.40.81.2 350 1050

13. -210 0 0 0.40.81.2 Time (s) F g,x (N) WALK 1.25 m/s Backward Forward 210

14. Net muscle moment at the ankle during a stance phase in locomotion  M ankle = I prox  M mus + M w - M Fg = I prox  M mus = I prox  - M w + M Fg I prox  & M w ---> segmental analysis & video M Fg ---> force platform & video FgFg FwFw M mus

15. Walking & running: stance versus swing M mus = I prox  - M w + M Fg Swing: M Fg = 0 Stance: M Fg large FgFg FwFw M mus

16. M Fg + M w MwMw

18. MwMw

21. Ankle net muscle moment: walk versus run Stance: extensor moments Run (250 Nm) >> Walk (120 Nm) Swing: net muscle moments ~ 0

22. Knee net muscle moment: walk versus run Stance: Run |M mus | >> Walk |M mus | Swing: small M mus in both

23. Summary of walking & running net muscle moments Run M mus >> Walk M mus Both: Stance M mus >> Swing M mus Both: Stance Ankle M mus > Knee M mus > Hip M mus Both: Swing Hip M mus > Knee M mus > Ankle M mus

25. U = ∫P mus dt

27. Running Ankle & Knee 1 st half of stance: muscles absorb power 2 nd half of stance: muscles produce power Specific roles Ankle is primary power producer Knee is primary power absorber Hip has very low power output

28. Leg COM Mechanical energy absorbed during first half of stance stored as elastic energy in muscles and tendons recovered in second half of stance

30. Walk: Inverted pendulum Passive conservation of mechanical energy reduction in muscle power requirements COM Leg

31. Walking net muscle power Net muscle power Walking <<< Running Ankle has greatest net power production end of stance

32. During walking, the knee joint generates 50Nm of extensor torque during the same interval of the stance phase when the knee joint moved from 0.14 rad of flexion to 0.2 rad of flexion in 0.02 s. Calculate the power of the knee joint muscles. a)50W b)-50W c)150 W d)-150 W

33. Is it better to walk with a flat COM?

38. Joint Work

39. Figure 3.34 Comparison of total joint torques during walking before and after ACL reconstruction controls (solid lines) 3 wks post (dotted lines) 6 months post (dashed lines)

40. Figure 3.33 Comparison of joint torques during walking before and after ACL reconstruction controls (solid lines) 3 wks post (dotted lines) 6 months post (dashed lines)

41. Figure 3.35 Comparison of joint powers during walking before and after ACL reconstruction controls (solid lines) 3 wks post (dotted lines) 6 months post (dashed lines)

43. Ankle Knee Hip

44. Does Oscar have an advantage? a) Yes b) No c) Does it matter? Ankle Knee Hip

45. Outline Muscle/Joint Mechanical work, power, & energy Definitions Examples Impulse-momentum Definition Examples

46. Impulse-Momentum Angular Momentum Principle of Impulse Momentum Conservation of Angular Momentum

47. Angular Momentum Linear Momentum (L) L=mv m:mass (kg) v:velocity (m/s) Units: kg-m/s vector Angular Momentum: quantity of angular motion of an object H=I  I: moment of Inertia  :angular velocity (rad/s) Units: kg-m 2 /s vector

48. Conservation of Angular Momentum When gravity is the only force acting on an object, angular momentum is conserved Angular momentum is conserved during flight H initial = H final I initial  initial = I final  final

49. If I changes,  changes I  Aerial Somersault About Transverse axis

51. Principle of Impulse-momentum Linear case Impulse =  mv F ave t=mv f -mv i Angular case Impulse =  I  T ave t=H f -H i When a torque is applied over a period of time, a change in angular momentum occurs Impulse = Change in Momentum

53. Tdt=d(H) T a v e t = H f - H i When a torque is applied over a period of time, a change in angular momentum occurs 95.3 kgm 2 /s or 92.4 kgm 2 /s Loss of – 33kgm 2 /s or 27.4 kgm 2 /s