# Total Body Centre of Gravity, Moment of Inertia and Angular Momentum

ESS2003 Kinesiology and Biomechanics II

Laboratory 5

**Total body centre of gravity, moment of inertia and angular momentum**

Dr Sharon Dixon

Aims:

- To calculate the height raised by the centre of gravity for a subject performing a back somersault.
- To calculate the moment of inertia and angular velocity for a trampolinist at two stages of a somersault.

## Task 1: Centre of gravity calculation using Hu-man software

This exercise will involve the digitisation of a gymnast performing a back somersault. You are required to digitise the somersault sequence. The Hu-man software uses this information, together with segmental masses and centres of gravity, to determine the total body centre of gravity using the segmentation method.

## Procedures

- Load the somersault data file

### Double click ‘Hu-m-an’ icon on desktop

### Click CD/Server Data Area

Select [gymnast] (OK) [backs02] (OK) backs02.avi (OK)

- Select the flight phase of the video sequence

In VIDEO-MODEL CONTROL window

- play the video sequence

- identify the frame numbers for take-off and landing

- in the box below ‘Start’ change the frame number to the take-off frame number

- in the box below ‘End’ change the frame number to the landing frame number

- Select *Utilities – Set a New Trial Sub-Sequence*

- Select Yes

- Select model for digitising

- Edit – Trial Set Up

### Under ‘List of Trial Set Up Titles’ - Select ‘11 Pt. Symmetric’

- Load – Yes – Exit

- Digitise the flight phase of the somersault

- Options – Digitise

### DIGITISE window will be active

- Select Scale, OK

- Input Real Length ‘1.8’

- Input Length Units ‘metres’

- Digitise the endpoints of the scaling object

- Select Apply New Scale

- using the left mouse button, select body landmarks as specified in the DIGITISE window

head, wrist, elbow, shoulder, hip, knee, ankle, toe, tip-toe, ball, heel

- click left mouse button to advance to the next frame

- if an error is made, click ‘re-digitise this frame’ to redigitise the whole frame

When all frames have been digitised, close the DIGITISE window.

- View the model

Using VIDEO-MODEL CONTROL window

- play the sequence to view the video and the model simultaneously

- select (tick) +Model

- view the sequence again

- Calculate total body centre of gravity

### Calculate – System C of G – 6 Segment Model

- Calculate

- Plot the time-history of the C of G

### In GRAPH DATA CONTROL window

- Select C of G Y: 6 Segment Model

Sketch the time-history of the vertical displacement of the total body centre of gravity in the space provided:

Questions:

- What is the height raised by the total body centre of gravity from take-off to peak height?

- The centre of gravity has been calculated for each frame using the segmentation method. Briefly describe the data required and the procedures used by the computer software to determine the total body centre of gravity from the digitised segment end-points.

Task 2:

*Table 1. Moment of inertia data (Dempster, 1955).*

Body SegmentMoment of Inertia about Segment

Centre of Gravity (kg.m2)

______

Head + Trunk2.2059

Upper Arm0.0213

Forearm + Hand0.0298

Thigh0.1052

Calf + Foot0.1613

*Procedures for the calculation of total body moment of inertia about whole body centre of gravity:*

1. Obtain segmental moments of inertia from Table 1, and input in the results table.

2. Use the mass ratios provided in the results table to calculate the segment masses (subject mass = 64.3 kg).

3. Measure the distance in mm from each body segment centre of gravity to the whole body centre of gravity and input these in the results table.

4. Measure the length of the 1 metre scale distance in mm, and use this to calculate a scale factor for converting from mm on the sheet to metres in real life.

5. Use this scale factor to determine the real distance from each segment centre of gravity to the total body centre of gravity (d). Input these lengths in the results table.

6. Calculate the transfer term (md2) for each segment, and input in results table.

7. Calculate the moment of inertia about the total body centre of gravity for each individual segment using the Parallel Axes Theorem (Icg = Is + md2 : Icg = total body moment of inertia about body centre of gravity; Is = segment moment of inertia about segment centre of gravity; m = mass of segment; d = distance from segment centre of gravity to whole body centre of gravity).

8. Sum the segment moments of inertia about the whole body centre of gravity, to calculate the total body moment of inertia.

Questions:

- What is the moment of inertia about the body centre of gravity for each of the body orientations provided?

- Given that the angular momentum of the trampolinist at take-off was 108.5 kg.m2.s-1, calculate the angular velocity for each of the two body positions.

*Procedures for calculation of angular velocity:*

Use Newton’s First Law for Angular Motion (Conservation of Angular Momentum):

‘A rotating body will continue to rotate with constant angular momentum unless acted on by an external moment’

(NB. Angular momentum (H) = I.)