Download Torques & Moments of Force

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
dS = 0.4 m
dW = 0.2 m
dFM = 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)