W9 - Angular Kinetics - Centre of Gravity Flashcards
Compare Newtons 1st law for linear & angular motion
L = Objects remains at rest or constant velocity unless acted on by an external force.
A = Rotating object will continue to do so at constant angular momentum unless acted on by an external force
Equation for Newtowns second law of motion
F = ma
Apply newtons 2nd law to LINEAR motion
A force applies to an object will cause the object to accelerate in proportion to that force.
Apply Newtons 2nd law to ANGULAR motion
An external moment produces an angular acceleration that is:
- Proportional to the moment
- In the direction of the moment
Apply newtons 3rd law to LINEAR motion
Every action has an equal + opposite reaction
Apply newtons 3rd law to ANGULAR motion
For every applied moment there is an equal + opposite reaction moment
Define moment/torque
Tendency of a force to cause rotation about a specific axis
Is a moment/torque a force?
NO
It’s the effect of a force in causing a rotation.
What is moment/torque also known as?
The measurement of a turning effect
What is the moment/torque a product of?
Magnitude of a force
+ perpendicular distance from line of action of force to axis of rotation.
How is moment calculated?
Mass x distance
Define eccentric force
Force whose line of action doesn’t pass through the centre of gravity
What does eccentric force always cause?
Rotation therefore a moment.
Eccentric force always causes rotation + therefore a moment.
What can it also cause?
Translation
What does Centric force have?
A line of action passing through axis of rotation/CoG
What is a couple?
2 equal + opposite parallel forces
When rotation occurs about body centre of gravity
What happens to the translation effects in a couple?
T effects fo each force cancel each other out = no translation
What is the moment effect of a couple?
Turning effect prod by a force couple
What does the amount of rotation in the moment effect of a couple depend on?
Magnitude of the forces
-But only need the mag. of 1 of the forces.
Perpendicular distance between lines of action.
Equation for the moment of a couple
M = F1 x distance
What is inertia in the linear case?
Objects tendency to resists a change in motion
Mass
What is inertia in the angular case?
Objects tendency to resist a change in motion
Moment of inertia
What are the 2 components of moments?
Magnitude of force
Perpendicular distance from pivot point to the line of action of the force
Units for moment
N.m
What is the resultant moment?
Sum of all moments about a defined point
What are clockwise moments conventionally?
-ive in direction
What are anti-clockwise moments conventionally?
+ive in direction
Define equilibrium
When all parts of the body are at rest or moving w/ the same constant velocity
What is the sum of moments when theres equilibrium?
0
What is the centre of gravity?
Point about which the gravitational force is balanced.
Where mass is EQUALLY distributed + through which the resultant force of gravity acts.
What are the 3 methods that can be used to ESTIMATE the location of an objects Centre of gravity?
Suspension Method
Reaction board method
Segmental method
Limitations to the suspension method
Not very practical
Cardboard cut outs only represent shape, not mass
What does the reaction board method employ?
Theory of equilibrium
How does the reaction board method employ the theory of equilibrium?
System is in equilibrium when nobody is on the board + when there is.
So, the forces + moments introduced by the person lying on the board must be in equilibrium.
Segmental method
What is required to calculate an objects centre of gravity location?
Coordinates of each segment endpoint
Segment weights
Locations of segment centres of gravity
What are the 3 main ways that segment data have been obtained for use with human participants in the past?
Cadaver data
Mathematical modelling
Scanning
Limitations to using cadaver data
Are the sampled population relevant?
How does cadaver storage influence characteristics?
Approach of finding centre of mass for 2 segments means the segment is considered 2D rather than 3D
Explain the mathematical modelling
Divides body into 17 segments
Differentiates between M + F
Accounts for varying densities
Allows subject-specific estimates
Scanning
Use of DXA to estimate segment properties
Limitations to scanning
Invasive
Costly
Time heavy
What is kinetics about?
Forces acting on the body
What can the forces acting on the body cause?
Rotation
Translation
or both
What does the segmental method theory make use of?
The fact that:
Resultant moment = Sum of moments
(Resultant: Moment of entire body acting around whole body CoG)
(Sum of moments: Each segment of body has a moment which we want to sum)
What do we calculate in the segmental method theory?
The moment for each segment:
Moment = force x distance
What is required to calculate an objects centre of gravity location?
Coordinates of each segment endpoint
Segment weights
Locations of segment centres of gravity
Do practise questions on sway slides
done?
What do moments about OY axis provide?
Horizontal location of CoG
X co-ordinate
What do moments about OX axis provide?
Vertical location of CoG
Y co-ordinate
