W10 - Angular kinetics - Moment of Inertia

Question 1

What is the rotational equivalent of mass?

Answer 1

Moment of inertia

Question 2

Define moment of inertia

Answer 2

Resistance of a body to a change in its angular motion

Question 3

What is the moment of inertia a measure of?

Answer 3

Distribution of mass about an axis

Question 4

How is moment of inertia calculated?

Answer 4

mr^2

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

Question 5

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

Answer 5

Less resistance to rotation = easier to alter angular motion

Question 6

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

Answer 6

Greater resistance to rotation = harder to alter angular motion

Question 7

What is the moment of inertia determined by?

Answer 7

Mass of body

Distribution of mass about CoG

Question 8

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

Answer 8

Slower

Question 9

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

Answer 9

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

Question 10

What is the parallel axis theorem used for?

Answer 10

To calculate moment of inertia

Question 11

What type of method does the parallel axis theorem use?

Answer 11

Segmental method

Question 12

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

Answer 12

Because they are connected to other segments.

Instead, they rotate about joint centres

Question 13

Equation for the parallel axis theorem

Answer 13

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

Question 14

Equation for the parallel axis theorem

What does the I(little A) represent?

Answer 14

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

Question 15

Equation for the parallel axis theorem

What does the I(little CG) represent?

Answer 15

Moment of inertia of segment about a segment CoG

Question 16

Equation for the parallel axis theorem

What does the m represent?

Answer 16

Segment mass

Question 17

Equation for the parallel axis theorem

What does the d represent?

Answer 17

Distance between axes of whole body CoG + segment CoG

Question 18

What can the parallel axis theorem be used to calculate?

Answer 18

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.

Question 19

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

Answer 19

Direct measurement

Ratio + regression

Mathematical modelling

Question 20

Direct measurement approach

List some papers that used this

Answer 20

Dempster (1995)

Chandler (1975)

Question 21

Direct measurement approach

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

Answer 21

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.

Question 22

Direct measurement approach

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

Answer 22

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

Question 23

Direct measurement approach

Equation that Chandler et al (1975) used

What does the I represent?

Answer 23

Moment of inertia about the axis of suspension

Question 24

Direct measurement approach

Equation that Chandler et al (1975) used

What does the m represent?

Answer 24

mass of subject

Question 25

Direct measurement approach Equation that Chandler et al (1975) used What does the g represent?

Answer 25

gravity = 9.81

Question 26

Direct measurement approach Equation that Chandler et al (1975) used What does the h represent?

Answer 26

Distance of mass centre from axis of suspension

Question 27

Direct measurement approach Equation that Chandler et al (1975) used What does the t represent?

Answer 27

Time for 1 oscillation

Question 28

Limitations to the direct measurement approach

Answer 28

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

Question 29

Ratio + Regression approach List some papers that used this approach

Answer 29

Hinrichs (1985) Yeadon + Morlock (1989)

Question 30

Ratio + Regression approach What is the idea of this approach?

Answer 30

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

Question 31

Ratio + Regression approach What does this approach provide a quick estimate of?

Answer 31

Subject specific inertia values

Question 32

Ratio + Regression approach Limitations

Answer 32

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

Question 33

Mathematical Modelling approach

Answer 33

Represents body as geometric solids of different shapes.

Question 34

Mathematical Modelling approach List examples of papers

Answer 34

Hanavan (1964) Jensen (1978)

Question 35

Mathematical Modelling approach Hanavan (1964) paper overview

Answer 35

Represented body as 15 simple geometric solids Model is personalised to participants by taking 25 anthropometric measurements as inputs to the model.

Question 36

Mathematical Modelling approach Hanavan (1964) paper What is assumed in this paper?

Answer 36

Uniform density of segments

Question 37

Mathematical Modelling approach Hanavan (1964) paper Hanavan model

Answer 37

Predicted CoG w/in 1.8cm of experimental data Predicted Mol w/in 10% of experimental data

Question 37

Mathematical Modelling approach Hanavan (1964) paper Hanavan model

Answer 37

Predicted CoG w/in 1.8cm of experimental data Predicted Mol w/in 10% of experimental data

Question 38

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

Answer 38

3 - 6 kgm2

Question 39

The parallel axis theorem allows the calculation of ...

Answer 39

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

Question 40

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

Answer 40

0.4 kgm2