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 

M

d 

F

Axis of Rotation

Moment Arm

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

M

d 

MOMENT

M = F * d 

F

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

M

MOMENT (Nm) is a vector; magnitude & direction

F

CCW

+ M

d  M = F * d  “Right-hand Rule”

M

CW

-

Right-hand Rule

M

CCW

+

Thumb Orientation: Positive Torques Up Out of the page Negative Torques Down Into the page

M

CCW

+

Moments at the Joint Level Static Equilibrium  M = 0 F m Known: Ws = 71 N W A&H d  S = 4 N = 0.4 m d  W = 0.2 m d  FM = 0.01 m  M = 0 W A&H W S Unknown: F m

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 M h d  CM M v Fh Known: Fv = 7500N Fh = 5000N d  = 0.4m

d  = 0.7m

d  Fv

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

M h Moments about the TBCM Long jump take-off d  CM Fh Known: Fh = 5000 N d  = 0.7 m Unknown: M h ___________________________ 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 CM Net Rotational Effect M Net M Net = M v + M h = 3000 Nm + (-3500 Nm) M Net = -500 Nm d  Fh d  Fv Angular Impulse Moment applied over a period of time  M cm  t = I cm 

Angular Impulse taken about an object’s CM = the object’s change in angular momentum Angular Momentum - the quantity of angular motion  M cm  M cm  M cm = I = I cm cm   t = I cm  /  t  where I cm the CM = moment of inertia, resistance to rotation about 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 Mv Fh Fv CM d  Mh d  Known: Fv = 1000 N Fh = 700 N d  = 0.3 m d  = 0.4 m

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

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

Fh M Net Fv Moments about the TBCM sprint start CM Net Rotational Effect M Net M Net = M v + M h = (-300 Nm) + (280 Nm) M Net = -20 Nm d  d  Angular Impulse Moment applied over a period of time  M cm  t = I cm 

Creating Rotation

Reposition your CM relative to Reaction Force

BACK Somersault F V d



d



F V F H

Horizontal RF Vertical RF -0.5

-0.4

2500 2000 1500 1000 500 -0.3

VRF

-0.2

-0.1

0 -500 0

Time Prior to Take-off (s)

time prior to take-off take-off 0.1

Rotational Demands of a Diver

Front Reverse Back Inward

Force primarily responsible for Net rotation: F V

F H

F V

F H

F V

F H

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)