ESS 303 – Biomechanics

Linear Kinematics

Linear VS Angular

Linear: in a

straight line (from

point A to point B)

Angular: rotational

(from angle A to

angle B)

A B

A

B

Kinematics VS Kinetics

Kinematics: description of motion

without regard for underlying forces

Acceleration

Velocity

Position

Kinetics: determination of the

underlying causes of motion (i.e., forces)

Linear Kinematics

The branch of biomechanics that deals with the description of the linear spatial and temporal components of motion

Describes transitional motion (from point A to point B)

Uses reference systems2D: X & Y axis3D: X, Y & Z axis

Linear Kinematics

A

B

What About This?

A

B

What About This?

A

B

Some Terms

Position: location in space relative to a reference

Scalars and vectorsScalar quantities: described fully by

magnitude (mass, distance, volume, etc)

Vectors: magnitude and direction (the position of an arrow indicates direction and the length indicates magnitude)

Some Terms

Distance: the linear measurement of space between points

Displacement: area over which motion occurred, straight line between a starting and ending point

Speed: distance per unit time (distance/time)Velocity: displacement per unit time or

change in position divided by change in time (displacement/time)

What About This?

A

BDistance & SpeedDistance & Speed

Displacement & VelocityDisplacement & Velocity

Graph Basics

A (1,1)

B (4,3)

C (5,2)

D (2,1)

X

Y

SI Units

Systeme International d’Units

Standard units used in science

Typically metricMass: Kilograms

Distance: Meters

Time: Seconds

Temperature: Celsius or kalvin

More Terms

Acceleration: change in velocity divided by change in time (Δ V / Δ t) (m/s)/sAcceleration of gravity: 9.81m/s2

Differentiation: the mathematical process of calculating complex results from simple data (e.g., using velocity and time to calculate acceleration)

Derivative: the solution from differentiation Integration: the opposite of differentiation (e.g.,

calculation of distance from velocity and time)

Today’s Formulas

Speed = d / tVelocity = Δ position / Δ tAcceleration = Δ V / Δ tSlope = rise / runResultant = √(X2 + Y2)

Remember: A2 + B2 = C2

SOH CAH TOASin θ = Y component / hypotenuseCos θ = X component / hypotenuseTan θ = Y component / X component θ

Sample Problems

A swimmer completes 4 lengths of a 50m poolWhat distance was traveled?What was the swimmer’s displacement?

Move from point (3,5) to point (6,8) on a graphWhat was the horizontal displacement?What was the vertical displacement?What was the resultant displacement?

Sample Problems

A runner accelerates from 0m/s to 4.7m/s in 3.2 secondsWhat was the runner’s rate of acceleration?

Someone kicks a football so that it travels at a velocity of 29.7m/s at an angle of 22° above the groundWhat was the vertical component of

velocity?What was the horizontal component of

velocity?