Biomechanics Exam 2

angular displacement (θ)

the change in angular position of an object as it rotates about an axis, measured in radians.

angular velocity (ω)

the rate of change of angular displacement of an object, typically measured in radians per second.

ω = Δθ / Δt

Angular acceleration (α)

the rate of change of angular velocity of an object, commonly measured in radians per second squared.

α = Δω / Δt

Right-hand rule

By aligning the right thumb with the axis of rotation and curling the fingers, the fingers point in the positive direction of motion. It is essential for standardizing kinematic data (e.g., knee flexion/extension).

Absolute angle

 angle that describes segment’s orientation in space (segment angle)

Relative angle

 angle at a joint between 2 adjacent segments (joint angle)

Law of Inertia (Newton’s First Law)

A body will maintain a state of rest or constant velocity unless acted on by an external force that changes the state

Inertia

The resistance to change in motion

Law of Acceleration (Newton’s second law)

A force applied to a body causes an acceleration proportional to the force, in the direction of the force, and inversely proportional to the body’s mass.

F=ma

Law of Reaction (Newton’s third law)

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

In terms of forces: When one body exerts a force on a second, the second body exerts a reaction force that is equal in magnitude and opposite in direction on the first body

Mass vs weight

mass = amount of matter

weight = force

Contact forces

Actions, pushes or pulls, exerted by one object in direct contact with another object (e.g., When a bat hits a baseball, or the foot hits the floor.)

friction & ground force reaction

Noncontact forces

Forces that act at a distance; Forces that are exerted by objects that are not in direct contact with one another and may be separated by a considerable distance (e.g., gravity)

Static analysis

Systems at rest or moving at a constant velocity

Acceleration = zero

Dynamic analysis

Accelerations ≠ zero

Horizontal (x) and vertical (y) acceleration components

Static vs Kinetic friction

Static friction: before motion occurs (larger)

Kinetic: during motion (smaller)

Momentum

Quantity of motion that an object has (p)

p = mass * velocity

Impulse

Change in momentum

When a force is applied to a body, the resulting motion is dependent on the magnitude of the applied force and the duration of force application.

J = Ft 

Impulse-momentum relationship

F Δt = (mv_final - mv_initial)

Work (W)

Force applied over a distance

W = F cosθ s

(𝜃 is angle between force vector and line of displacement (may not have an angle: cos 0° =1)).

Power (P)

Work done per unit of time

P =  Δw/Δt    

Kinetic Energy (KE)

Energy resulting from motion, it has velocity

KE=  1/2 mv^2 

Any change in velocity will affect the amount of energy in the object

Potential energy (PE)

Capacity to do work because of position, “stored energy”

PE = mgh

(m = mass; g = gravity (9.81); h = height)

Total energy = ?

KE + PE

Strain energy (SE)

SE =  1/2  kx^2

k is the proportionality constant, or stiffness and x is the distance over which the object is deformed

k depends on the material deformed and represents the object’s ability to store energy

Impact

The collision of two bodies over a small time interval during which the two bodies exert large forces on each other.

Two types of impact

Elastic and inelastic collisions.

Elastic collision

The velocities of the two bodies after impact are the same as their relative velocities before impact; No kinetic energy is lost

Ex: The impact of a bouncy ball with a hard surface approaches perfect elasticity

Inelastic (plastic) collision

At least one of the bodies deforms and does not regain its original shape, and the bodies do not separate; Kinetic energy is lost (heat or sound).

Conservation of Momentum

In the absence of external forces, the total momentum of a given system remains constant

m₁v₁ = m₂v₂

Can assist us in calculating velocity after a collision

Coefficient of Restitution (CoR)

CoR describes the elasticity of an impact and the interaction between two bodies during impact.

–Unitless number between 0 and 1

–Closer to 1: more elastic

–Closer to 0: more inelastic