for a man of mass 75kg and height 185 cm claculate the following using standard anthropometric data.
1. length of his upper arm
2. mass of his upper arm
3. position of the centre of mass of his upper arm relative to the glenohumeral joint
4. radius of gyration of his upper arm about his glenohumeral joint
5. moment of inertia of his upper arm about his glenohumeral joint
To calculate the measurements and properties of the upper arm using standard anthropometric data, we need to utilize average or representative values. Keep in mind that these calculations are estimates, as individual variations can occur.
1. Length of the Upper Arm:
The average ratio of total arm length to total height is approximately 0.295 for males. We can use this value to estimate the length of the upper arm by multiplying it with the person's height.
Length of Upper Arm = 0.295 * Height
Length of Upper Arm = 0.295 * 185 cm
2. Mass of the Upper Arm:
The percentage of total body mass corresponding to the upper arm is generally around 2.7% for males. To calculate the mass of the upper arm, multiply the person's body mass by this percentage.
Mass of Upper Arm = 2.7% * Body Mass
Mass of Upper Arm = 2.7% * 75 kg
3. Position of the Centre of Mass of the Upper Arm:
The center of mass of the upper arm typically lies at approximately 43% of the total upper arm length, starting from the glenohumeral joint. Calculate the position of the center of mass by multiplying the length of the upper arm by this percentage.
Position of Center of Mass = 43% * Length of Upper Arm
Position of Center of Mass = 43% * (0.295 * 185 cm)
4. Radius of Gyration of the Upper Arm:
The radius of gyration provides an indication of how the mass is distributed relative to the axis of rotation. For the upper arm, the ratio of the radius of gyration to the length is about 0.41. Calculate the radius of gyration by multiplying the length of the upper arm by this ratio.
Radius of Gyration = 0.41 * Length of Upper Arm
Radius of Gyration = 0.41 * (0.295 * 185 cm)
5. Moment of Inertia of the Upper Arm:
The moment of inertia is a measure of an object's resistance to changes in rotational motion. To calculate the moment of inertia of the upper arm about the glenohumeral joint, we assume it can be treated as a cylindrical rod.
Moment of Inertia = (1/3) * Mass * (Radius of Gyration)^2
Moment of Inertia = (1/3) * (2.7% * Body Mass) * ((0.41 * Length of Upper Arm)^2)
Please note that these calculations are based on average or representative values and may not precisely reflect actual measurements for an individual.