Chapter 3: Principles of Biomechanics

What are the two components of Newton’s 1st law: law of inertia

Linear and rotational

Law of inertia (linear)

A body remains at rest or in constant linear velocity except when compelled by an external force

Law of inertia (rotational)

A body remains at rest or in constant angular velocity around an axis except when compelled by an external torque

Static equilibrium

Linear and rotational velocities are zero and accelerations are zero

Dynamic equilibrium

Linear and rotational velocities are constant and not zero and accelerations are zero

Inertia

An object’s resistance to a change in its state of motion (due to mass/momentum)

Center of mass

Point about which mass is most evenly distributed in all directions (within the object)
Slightly anterior to S2 in the human body (when in anatomical position)

Center of gravity

Point about which the effects of gravity are most completely balanced

Mass moment of inertia

A body’s resistant to change in angular velocity
Depends on mass and distribution of mass with respect to an axis of rotation
Units of kg*m²

Equation for mass moment of inertia

n indicates the number of parts in the body
m_i is the mass of each part
r_i is the distance of each part to the axis of rotation

Mass moment of Inertia and “Conservation of Angular Momentum”

By reducing the mass moment of inertia, trunk position increases angular velocity
Fully extended positions increase the mass moment of inertia, thereby decreasing angular velocity

Newton’s 2nd Law: Acceleration

The linear acceleration of a body is directly proportional to the force causing it, takes place in the same direction in which force acts, and is inversely proportional to the mass of the body

Impulse-Momentum Relationship

Derived from Newton’s 2nd law
Momentum: quantity of motion possessed by a body
Mass of moment of inertia * angular velocity
Linear impulse: product of force and time, measure of what is required to change the momentum of a body

Mechanical work

Occurs when force or torque operates over some linear or angular displacement
No movement = no mechanical work done
Does not take into account the time force or torque is applied
Mechanical work units are joules (J)

Power

Power is the rate of performing work over time
Average power = work/time
Instantaneous linear power = force * linear velocity
Instantaneous angular power = torque * angular velocity

Newton’s 3rd Law: Action-Reaction

For every reaction there is an equal and opposite reaction
Implies every effect one body segment exerts on another is simultaneously counteracted by the second body segment exerts on the first
Consequences is based on F=ma

Free body diagrams

Assume rigid segments that are rigidly connected in static equilibrium