Torques & Moments of Force
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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 Force (N) applied a perpendicular distance (m) from the axis of rotation. M = F * d F M d Axis of Rotation Moment Arm d (m) Perpendicular distance from the point of force application to the axis of rotation d d d MOMENT M = F * d F d Known: F = 100 N d = 0.25 m Unknown: M _____________________ M M = 100 N * 0.25 m M = 25 Nm MOMENT (Nm) is a vector; magnitude & direction F CCW + d M M = F * d “Right-hand Rule” M CW M - Right-hand Rule CCW + M Thumb Orientation: Positive Torques Up Out of the page Negative Torques Down Into the page Moments at the Joint Level Static Equilibrium M = 0 Known: Ws = 71 N W A&H = 4 N dS = 0.4 m dW = 0.2 m dFM = 0.01 m M = 0 CCW + M Fm WA&H WS Unknown: Fm 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 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. 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 Moments about the total body center of mass (TBCM) Long jump take-off Mh Known: Fv = 7500N Fh = 5000N Mv CM d = 0.4m d Fh d Fv d = 0.7m Moments about the TBCM Long jump take-off Known: Fv = 7500N d = 0.4m Mv CM Unknown: Mv ___________________________ d M v = Fv * d Fv M v = 7500 N * 0.4 m M v = 3000 Nm (+) Moments about the TBCM Long jump take-off Known: Fh = 5000 N d = 0.7 m Mh CM d Unknown: Mh Fh ___________________________ M h = Fh * d M h = 5000 N * 0.7 m M h = 3500 Nm (-) Moments about the TBCM Long jump take-off M Net Net Rotational Effect M Net = Mv + Mh M Net = 3000 Nm + (-3500 Nm) M Net = -500 Nm CM d Fh d Fv Angular Impulse Moment applied over a period of time Mcm t = Icm 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. Moments about the TBCM sprint start Known: Fv = 1000 N Fh = 700 N Mv CM Mh d Fh Fv d d = 0.3 m d = 0.4 m Moments about the TBCM sprint start Known: Fv = 1000 N Mv d = 0.3 m CM Unknown: Mv ___________________________ Fv d M v = Fv * d M v = 1000 N * 0.3 m M v = 300 Nm (-) Moments about the TBCM sprint start Known: Fh = 700 N d = 0.4 m CM Mh Fh d Unknown: Mh ___________________________ M h = Fh * d M h = 700 N * 0.4 m M h = 280 Nm (+) Moments about the TBCM sprint start M Net CM d Fh Fv d Net Rotational Effect M Net = Mv + Mh M Net = (-300 Nm) + (280 Nm) M Net = -20 Nm Angular Impulse Moment applied over a period of time Mcm t = Icm Creating Rotation Reposition your CM relative to Reaction Force Horizontal RF 2500 Vertical RF 2000 BACK Somersault Force (N) d FH FV time prior to take-off 1500 d FV take-off 1000 500 -0.5 -0.4 -0.3 VRF -0.2 0 -0.1 Time Prior to Take-off (s) -500 0 Rotational Demands of a Diver Front Reverse Back Inward FH Force primarily responsible for Net rotation: FV FV FH FV FH 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)
