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Torques, Moments of Force, & Angular Impulse

Torques, Moments of Force, & Angular Impulse. Course Reader: p. 61 - 85. Causes of Motion. Linear Translation F = m*a. What happens when you move the point of force application? . Causes of Motion. MOMENT (N*m): cause of angular rotation

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Torques, Moments of Force, & Angular Impulse

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  1. Torques, Moments of Force, & Angular Impulse Course Reader: p. 61 - 85

  2. Causes of Motion Linear Translation F = m*a What happens when you move the point of force application?

  3. Causes of Motion MOMENT (N*m): cause of angular rotation Force (N) applied a perpendicular distance (m) from the axis of rotation. M = F * d F M d

  4. Axis of Rotation

  5. Moment Armd (m) Perpendicular distance from the point of force application to the axis of rotation d d d

  6. F d M MOMENTM = F * d Known: F = 100 N d = 0.25 m Unknown: M _____________________ M = 100 N * 0.25 m M = 25 Nm

  7. F d M M M MOMENT (Nm) is a vector; magnitude & direction CCW + CW - M = F * d “Right-hand Rule”

  8. CCW + M Right-hand Rule Positive Torques Up Out of the page Negative Torques Down Into the page Thumb Orientation:

  9. Fm CCW + WA&H WS M Moments at the Joint LevelStatic EquilibriumM = 0 Known: Ws = 71 N W A&H = 4 N dS = 0.4 m dW = 0.2 m dFM = 0.01 m M = 0 Unknown: Fm

  10. Axis of Rotation: Center of Mass Center of Mass (CM, CoG, TBCM) • The balance point of an object Object of uniform density; CM is located at the Geometric Center

  11. Axis of Rotation: Center of Mass Center of Mass (CM, CoG, TBCM) • The balance point of an object Object of non-uniform density; CM is dependent upon mass distribution & segment orientation / shape.

  12. Axis of Rotation: TBCM CM location is dependent upon mass distribution & segment orientation Moments are taken about the total body center of mass. CM CM CM CM

  13. Mv Mh d Fh d Fv Moments about the total body center of mass (TBCM)Long jump take-off Known: Fv = 7500N Fh = 5000N d = 0.4m d = 0.7m CM

  14. Mv d Moments about the TBCMLong jump take-off Known: Fv = 7500N d = 0.4m Unknown: Mv ___________________________ M v = Fv * d M v = 7500 N * 0.4 m M v = 3000 Nm (+) CM Fv

  15. Mh d Moments about the TBCMLong jump take-off Known: Fh = 5000 N d = 0.7 m Unknown: Mh ___________________________ M h = Fh * d M h = 5000 N * 0.7 m M h = 3500 Nm (-) CM Fh

  16. d Fh d Fv Moments about the TBCMLong jump take-off Net Rotational Effect M Net = Mv+Mh M Net = 3000 Nm+ (-3500 Nm) M Net = -500 Nm M Net CM Angular Impulse Moment applied over a period of time Mcm t = Icm 

  17. Angular Impulse taken about an object’s CM = the object’s change in angular momentum Angular Momentum - the quantity of angular motion Mcm = Icm  Mcm = Icm  / t Mcm t = Icm  where Icm = moment of inertia, resistance to rotation about the CM Note: The total angular momentum about the TBCM remains constant. An athlete can control their rate of rotation (angular velocity) by adjusting the radius of gyration, distribution (distance) of segments relative to TBCM.

  18. Mv Mh d Fh d Fv Moments about the TBCMsprint start Known: Fv = 1000 N Fh = 700 N d = 0.3 m d = 0.4 m CM

  19. Mv Moments about the TBCMsprint start Known: Fv = 1000 N d = 0.3 m Unknown: Mv ___________________________ M v = Fv * d M v = 1000 N * 0.3 m M v = 300 Nm (-) CM d Fv

  20. Mh Moments about the TBCMsprint start Known: Fh = 700 N d = 0.4 m Unknown: Mh ___________________________ M h = Fh * d M h = 700 N * 0.4 m M h = 280 Nm (+) CM d Fh

  21. d Fh d Fv Moments about the TBCMsprint start Net Rotational Effect M Net = Mv+Mh M Net = (-300 Nm)+ (280 Nm) M Net = -20 Nm M Net CM Angular Impulse Moment applied over a period of time Mcm t = Icm 

  22. time prior to take-off take-off Creating RotationReposition your CM relative to Reaction Force BACK Somersault d VRF FH d FV FV

  23. Rotational Demands of a Diver Front Reverse Back Inward FH FV Force primarily responsible for Net rotation: FV FV FH FH

  24. Take-home Messages • M (Nm) = F (N) * d (m) • Right-hand Rule: used to determine moment direction • Static Equilibrium: M = 0 • Center of Mass (CM, TBCM) • balance point of an object • Position dependent upon mass distribution & segment orientation • At the total-body level, moment created by the GRF’s taken about TBCM. Where moment arm length = perpendicular distance from CP location to TBCM location (dx & dy) • Moments are generated to satisfy the mechanical demands of a given task (total body, joint level, etc)

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