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Yr 2 - Biomechanics > W10 - Angular kinetics - Moment of Inertia > Flashcards

W10 - Angular kinetics - Moment of Inertia Flashcards

1
Q

What is the rotational equivalent of mass?

A

Moment of inertia

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2
Q

Define moment of inertia

A

Resistance of a body to a change in its angular motion

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3
Q

What is the moment of inertia a measure of?

A

Distribution of mass about an axis

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4
Q

How is moment of inertia calculated?

A

mr^2

m = mass of object
r = perpendicular distance from mass to axis of rotation
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5
Q

What happens in regards to moment of inertia when the mass is concentrated CLOSER to the axis?

A

Less resistance to rotation = easier to alter angular motion

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6
Q

What happens in regards to moment of inertia when the mass is concentrated FURTHER away from the axis of rotation?

A

Greater resistance to rotation = harder to alter angular motion

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7
Q

What is the moment of inertia determined by?

A

Mass of body

Distribution of mass about CoG

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8
Q

If a person is spinning with their arms out compared to in, is their spin faster or slower?

A

Slower

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9
Q

Why is it more difficult to rotate in a straight position for a gymnast than in a tucked?

A

Because more mass is distributed further away from the axis of rotation.

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10
Q

What is the parallel axis theorem used for?

A

To calculate moment of inertia

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11
Q

What type of method does the parallel axis theorem use?

A

Segmental method

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12
Q

Why don’t segments of the body rotates about their own centres of gravity?

A

Because they are connected to other segments.

Instead, they rotate about joint centres

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13
Q

Equation for the parallel axis theorem

A

I(little A) = I (little CG) + md^2

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14
Q

Equation for the parallel axis theorem

What does the I(little A) represent?

A

Moment of inertia of the body rotating about A (CoG of whole body)

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15
Q

Equation for the parallel axis theorem

What does the I(little CG) represent?

A

Moment of inertia of segment about a segment CoG

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16
Q

Equation for the parallel axis theorem

What does the m represent?

A

Segment mass

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17
Q

Equation for the parallel axis theorem

What does the d represent?

A

Distance between axes of whole body CoG + segment CoG

18
Q

What can the parallel axis theorem be used to calculate?

A

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.

19
Q

Data from what techniques were used to estimate the moment of inertia of a person?

A

Direct measurement

Ratio + regression

Mathematical modelling

20
Q

Direct measurement approach

List some papers that used this

A

Dempster (1995)

Chandler (1975)

21
Q

Direct measurement approach

What did Chandler et al (1975) do in their paper?

A

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.

22
Q

Direct measurement approach

What was the equation that Chandler et al (1975) used?

A

I = (mghT^2) / (4 x pi^2)

23
Q

Direct measurement approach

Equation that Chandler et al (1975) used

What does the I represent?

A

Moment of inertia about the axis of suspension

24
Q

Direct measurement approach

Equation that Chandler et al (1975) used

What does the m represent?

A

mass of subject

25
Q

Direct measurement approach

Equation that Chandler et al (1975) used

What does the g represent?

A

gravity = 9.81

26
Q

Direct measurement approach

Equation that Chandler et al (1975) used

What does the h represent?

A

Distance of mass centre from axis of suspension

27
Q

Direct measurement approach

Equation that Chandler et al (1975) used

What does the t represent?

A

Time for 1 oscillation

28
Q

Limitations to the direct measurement approach

A

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

29
Q

Ratio + Regression approach

List some papers that used this approach

A

Hinrichs (1985)

Yeadon + Morlock (1989)

30
Q

Ratio + Regression approach

What is the idea of this approach?

A

Take existing cadaveric data + ID regression equations that allow researchers to estimate inertia values based o subject-specific characteristics.

i.e segment length

31
Q

Ratio + Regression approach

What does this approach provide a quick estimate of?

A

Subject specific inertia values

32
Q

Ratio + Regression approach

Limitations

A

Same as the direct measurement approach due to equations being derived from that approach.

33
Q

Mathematical Modelling approach

A

Represents body as geometric solids of different shapes.

34
Q

Mathematical Modelling approach

List examples of papers

A

Hanavan (1964)

Jensen (1978)

35
Q

Mathematical Modelling approach

Hanavan (1964) paper overview

A

Represented body as 15 simple geometric solids

Model is personalised to participants by taking 25 anthropometric measurements as inputs to the model.

36
Q

Mathematical Modelling approach

Hanavan (1964) paper

What is assumed in this paper?

A

Uniform density of segments

37
Q

Mathematical Modelling approach

Hanavan (1964) paper

Hanavan model

A

Predicted CoG w/in 1.8cm of experimental data

Predicted Mol w/in 10% of experimental data

37
Q

Mathematical Modelling approach

Hanavan (1964) paper

Hanavan model

A

Predicted CoG w/in 1.8cm of experimental data

Predicted Mol w/in 10% of experimental data

38
Q

What would you estimate the moment of inertia of a gymnast performing a somersault in the tucked position to be?

A

3 - 6 kgm2

39
Q

The parallel axis theorem allows the calculation of …

A

the moment of inertia of a segment about a point of rotation

40
Q

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

A

0.4 kgm2

Yr 2 - Biomechanics (7 decks)

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