DEFINITIONS & EQUATIONS

The following definitions and equations have been included within the blog to allow a novice learner in the field of biomechanics a greater basic understanding of the terminology and how they work.

Definitions

acceleration rate of change in velocity over the change in time

angular acceleration rate of change of angular velocity; equal to angular velocity per unit of time

angular displacement change in angular position or the orientation of a straight segment

angular impulse product of torque and time (torque produced over a period of time); equal to the change in angular momentum of an object

angular momentum product of the moment of inertia and angular velocity; angular analogue of linear momentum

angular velocity rate of change in angular displacement; equal to angular displacement per unit time

axis of rotation imaginary line passing through the centre of rotation; perpendicular to the plane of rotation

biomechanics field of science devoted to understanding mechanical principles in relation to biological organisms

centre of gravity point about which the sum of torques if all points weights (that is, mass × gravity) of a body equals zero; the body can balance at this point

centre of mass point about which the sum of torques of all point weights of a body would be zero if oriented perpendicular to the line of gravity

efficiency ratio of the input to output of a system; often refers to ratio of energy in to energy out

force product of mass and acceleration; induces a change in the mobile state of an object

impulse product of applied force and the time over which it is applied

impulse-momentum relationship relationship between impulse and momentum; the momentum of an object will change in proportion to the sum of applied impulses

inertia tendency for a body to remain in its present state of motion

kinetic chain linked segments of a body that move together

linear straight or curved but not circular (rotational) path

linear acceleration rate of change of linear velocity; equal to angular velocity per unit time

linear displacement change in linear position or the orientation of a straight segment

linear momentum product of the mass and linear displacement; equal to linear displacement per unit of time

linear velocity rate of change in linear displacement; equal to linear displacement per unit time

mass quantity of matter in an object

moment of inertia tendency for a rotating body to remain in its present state of motion; equal to the product of the mass if an object and its radius of gyration

moment of force (torque) the result of a force acting at a distance from a centre of rotation; rotational action of a force

Newton's Law's

First: An object will remain at rest or continue to move with constant velocity as long as the net force equals zero. 

Second: The acceleration of an object is proportional to the net force acting on it and inversely proportional to the mass of the object.

Third: For every action, there is an equal and opposite reaction.

power rate of doing work; work per unit or the product of force and velocity

push-like movement pattern pattern of movement whereby the joints linked segments extend (or flex) simultaneously; optimum pattern for high force and accuracy

radius of gyration distance from the axis of rotation to a point where the centre of mass of the object could be located without altering its rotational characteristics

recovery phase period during which an appendage is repositioned from the back to the front of the boy in preparation for the swing phase

rotation circular (non-linear) motion or motion about an axis of rotation

speed rate of change of distance, without reference to direction

swing phase period during which an appendage is repositioned from the front to the back of the body; usually associated with the application of propulsive force

throw-like movement pattern patter of movement whereby the joints of linked segments extend (or flex) in a sequential order, usually proximo-distally; optimum pattern for the attainment of high movement speeds

trajectory flight path of a projectile

translation linear motion

Equations

speed Δd/Δt

velocity (v) Δs/Δt

acceleration (a) Δv/Δt

angular velocity (ω) Δθ/Δt

angular acceleration (α) Δω/Δt or τ/I

force (F) m×a

torque (moment of force) (τ) F×d, where d is the moment arm of force, or τ = Iα

sum of moments or sum of torque (ΣM or Στ) τ_t = τ₁ + τ₂ + τ₃ ...

momentum (M) m×v

angular momentum (H or L) Iω or mk²ω

angular impulse-momentum relationship τ∙t = Iω

impulse (J) F×t or Δmv

inertia m

moment of inertia (I) Σmr² or mk²

power (P) F×v or W/t

All definitions and equations found in Blazevich's (2010) Sports Biomechanics.