W10 - Angular kinetics - Moment of Inertia Flashcards
What is the rotational equivalent of mass?
Moment of inertia
Define moment of inertia
Resistance of a body to a change in its angular motion
What is the moment of inertia a measure of?
Distribution of mass about an axis
How is moment of inertia calculated?
mr^2
m = mass of object r = perpendicular distance from mass to axis of rotation
What happens in regards to moment of inertia when the mass is concentrated CLOSER to the axis?
Less resistance to rotation = easier to alter angular motion
What happens in regards to moment of inertia when the mass is concentrated FURTHER away from the axis of rotation?
Greater resistance to rotation = harder to alter angular motion
What is the moment of inertia determined by?
Mass of body
Distribution of mass about CoG
If a person is spinning with their arms out compared to in, is their spin faster or slower?
Slower
Why is it more difficult to rotate in a straight position for a gymnast than in a tucked?
Because more mass is distributed further away from the axis of rotation.
What is the parallel axis theorem used for?
To calculate moment of inertia
What type of method does the parallel axis theorem use?
Segmental method
Why don’t segments of the body rotates about their own centres of gravity?
Because they are connected to other segments.
Instead, they rotate about joint centres
Equation for the parallel axis theorem
I(little A) = I (little CG) + md^2
Equation for the parallel axis theorem
What does the I(little A) represent?
Moment of inertia of the body rotating about A (CoG of whole body)
Equation for the parallel axis theorem
What does the I(little CG) represent?
Moment of inertia of segment about a segment CoG
Equation for the parallel axis theorem
What does the m represent?
Segment mass
Equation for the parallel axis theorem
What does the d represent?
Distance between axes of whole body CoG + segment CoG
What can the parallel axis theorem be used to calculate?
Moment of inertia of a segment about a joint centre.
i.e thigh about hip
OR
Moment of inertia of a whole body about a point of rotation.
i.e body about its centre of gravity.
Data from what techniques were used to estimate the moment of inertia of a person?
Direct measurement
Ratio + regression
Mathematical modelling
Direct measurement approach
List some papers that used this
Dempster (1995)
Chandler (1975)
Direct measurement approach
What did Chandler et al (1975) do in their paper?
Segmented 6 cadavers
Then suspended by string + swung
Duration of each oscillation was recorded to allow calculation of the moment of inertia using an equation.
Direct measurement approach
What was the equation that Chandler et al (1975) used?
I = (mghT^2) / (4 x pi^2)
Direct measurement approach
Equation that Chandler et al (1975) used
What does the I represent?
Moment of inertia about the axis of suspension
Direct measurement approach
Equation that Chandler et al (1975) used
What does the m represent?
mass of subject
Direct measurement approach
Equation that Chandler et al (1975) used
What does the g represent?
gravity = 9.81
Direct measurement approach
Equation that Chandler et al (1975) used
What does the h represent?
Distance of mass centre from axis of suspension
Direct measurement approach
Equation that Chandler et al (1975) used
What does the t represent?
Time for 1 oscillation
Limitations to the direct measurement approach
Varying definitions of segments start + end points in the literature
Sample may not be representative of the population interested in
Highly invasive + difficult process makes it unfeasible to obtain from varied populations
Ratio + Regression approach
List some papers that used this approach
Hinrichs (1985)
Yeadon + Morlock (1989)
Ratio + Regression approach
What is the idea of this approach?
Take existing cadaveric data + ID regression equations that allow researchers to estimate inertia values based o subject-specific characteristics.
i.e segment length
Ratio + Regression approach
What does this approach provide a quick estimate of?
Subject specific inertia values
Ratio + Regression approach
Limitations
Same as the direct measurement approach due to equations being derived from that approach.
Mathematical Modelling approach
Represents body as geometric solids of different shapes.
Mathematical Modelling approach
List examples of papers
Hanavan (1964)
Jensen (1978)
Mathematical Modelling approach
Hanavan (1964) paper overview
Represented body as 15 simple geometric solids
Model is personalised to participants by taking 25 anthropometric measurements as inputs to the model.
Mathematical Modelling approach
Hanavan (1964) paper
What is assumed in this paper?
Uniform density of segments
Mathematical Modelling approach
Hanavan (1964) paper
Hanavan model
Predicted CoG w/in 1.8cm of experimental data
Predicted Mol w/in 10% of experimental data
Mathematical Modelling approach
Hanavan (1964) paper
Hanavan model
Predicted CoG w/in 1.8cm of experimental data
Predicted Mol w/in 10% of experimental data
What would you estimate the moment of inertia of a gymnast performing a somersault in the tucked position to be?
3 - 6 kgm2
The parallel axis theorem allows the calculation of …
the moment of inertia of a segment about a point of rotation
Calculate the moment of inertia of the thigh about the hip joint centre:
Segment length = 0.5m
Distance of hip joint centre to thigh CofG = 0.2m
Body mass = 75kg
Thigh mass = 10% of body mass
MofI of thigh sgement about segment CofG = 0.1 kgm2
0.4 kgm2
