Foundations of Human Movement - Unit 2

Kinematics

Describing the displacement of a segment/describes the motion

Kinetics

Finding out the cause of the motion

Linear kinematics

Projectile motion such as jumping forward

Angular kinematics

Rotations (subject’s orientation is changed with the axis of rotation)

Linear kinetics

Gravity, friction, momentum, energy, work

Angular kinetics

Torque, inertia, momentum

Scalar

Only magnitude

Vector

Magnitude and direction

5 kinematic variables that fully describe the motion of a segment

Type of displacement
Direction of displacement
Magnitude of displacement
Velocity
Acceleration

Velocity vs speed

Speed is scalar, velocity is vector

Linear displacement - linear motion

Movement of a segment in a straight line
Rare in human movement (segments of body are neither unconstrained nor isolated; some rotary motion of segment usually occurs even if it isn’t visible)

Distance

d
actual traveled linear path (even if the motion was not linear, it measures the linear path from point A to point B)

Displacement

p
Change in position

Speed

s
Distance per unit time regardless of direction
s = ‘d’ / ‘t2 - t1’

Velocity

v
Displacement per unit time in a given direction
v = change in displacement / change in time

Acceleration

a
Change in velocity per unit time
a = change in velocity / change in time

Characteristics of projectile motion

Since most objects are released at an angle, horizontal and vertical components of displacement, velocity, and acceleration have to be analyzed separately
Velocity of x is constant, therefore acceleration of x is 0
Acceleration of y = acceleration of g = -9.81 m/s²
Release speed, angle, and height affect projectile motion
Optimum release angle is 45 degrees when release and landing heights are the same
At same height, velocity of y is going up and coming down are same in magnitude but opposite in direction
Velocity at peak is zero

Variables and characteristics of projectile motion

On the way up:
Vi = max velocity
Vf = 0
Pi - 0
Pf - max height
t = ½ of flight time
a = -9/81

On the way down:
Vi = 0
Vf = max velocity
Pi = max height
Pf = 0
t = ½ of flight time
a = -9.81

Trigonometry

Sin = O/H
Cos = A/H
Tan = O/A

In projectile motion problems, the ‘O’ is the vertical velocity
When trying to find the angle, you have to use the inverse functions

angular motion

Movement of a segment around a fixed axis in a curved path
Fixed axis called center of rotation
True rotary motion in human movement is rare (can occur only if the segment is prevented from translating and is forced to rotate about a fixed axis

general motion in angular kinematics

Combination of rotation and translation
Curvilinear and 3d motion
Most joint rotations take place around a series of instantaneous center of rotation

curvilinear

Motion in two dimensions
Axis about which movement occurs shifts in space as object moves and is called instantaneous center of rotation

3D motion

Occurs around a helical axis of motion

Magnitude of displacement in angular kinematics

Magnitude of angular displacement can be expressed in degrees or radians and is called the range of motion (ROM)
One radian = 57.3 degrees
1 degree = 0.01745 radians
1 revolution = 2*pi*1radian = 360 degrees

Relative angle in angular kinematics

The angle of one body segment relative to another body segment articulating at the joint
Used to quantify ROM

Absolute angle in angular kinematics

The angle of one body segment relative to a fixed line of reference

Distance in angular kinematics

Actual traveled linear path
O with line vertical line through it (phi)
Units are radians or degrees

Displacement in angular kinematics

Change in angular position
O with a horizontal line through it (theta)
Units are radians or degrees

Speed in angular kinematics

Angular distance per unit time regardless of direction
lowercase sigma = d/t2 - t1
units: rad/s or deg/s

Velocity in angular kinematics

Angular displacement per unit time in a given direction
ω (lowercase omega) = change in displacement over change in time
Units: rad/s or deg/s

Acceleration in angular kinematics

Change in angular velocity per unit time
α (lowercase alpha) = change in velocity over change in time
Units: rad/s² or deg/s²

Is counterclockwise direction denoted as positive or negative?

positive

Is clockwise direction denoted as positive or negative in angular motion?

negative

Relationships between Linear and Angular Kinematics

Linear and angular displacement: d = r(theta)

Linear and angular velocity: v = r(lowercase omega in radians/s) [direction is tangent to the arc]

Linear and angular acceleration: a(tangential) and a(radial)

kinetics

Movement of a body segment with regard to force
In human motion, there are multiple segments and multiple forces that are usually applied to two or more segments simultaneously
We can create a visual representation of all these forces (free-body diagram)

free-body diagram

proportional representation of all forces
need to be able to draw one in order to solve a question
M = angular force
Arrow always represents force

Forces

Anytime two objects make contact, they will either push or pull each other with some magnitude of force (represented by the units Newtons or pounds—Newtons in this class)

1 pound (lb) = ____N

4.5

external forces

Pushes or pulls on the body that arise from outside the body such as gravity, wind, other ppl, the push of floor on the feet, etc.)

Internal forces

Act on the structures of the body and arise from the body’s own structures
Essential for initiation of movement
Counteract movement produced by external forces as well as other internal forces

Force vectors

All forces are vector quantities and contain three characteristics when drawn:
1. Point of application (location of base of arrow)
2. Direction/orientation (orientation of arrow; direction of force being exerted)
3. Magnitude (length of arrow; amount of force being exerted)

Gravity

The influence or attractive force of the earth on all bodies near to its surface
Body weight = force of gravity [F(g)] = mass in kg*-9.81 [m*a(g)]
Acceleration due to gravity = a(g) = -9.81 m/s²

Force of gravity

Gravity is a vector pointing vertically downward toward center of earth (often referred to as the line of gravity/LOG)
The point of application is at the center of mass (COM) of that object

Center of mass

Hypothetical location at which mass is concentrated

Center of mass of the human body

Lies approximately anterior to S2, assuming body is a single rigid object. This does not change regardless of body position.
The LOG changes its relative position within the body and with the base of support (i.e., whatever you’re standing on) rather than the COM changing

COM, LOG, and Stability

For an object to be stable, the LOG must fall within the base of support
When the LOG is outside the base of support (such as the area beneath your foot), the object will be unstable
Ex: A football player is unstable bc his LOG is anterior to his base of support which is only the ground beneath his left tippy toe, and his COM is above S2 in the position he’s in
When the base of support is large, the LOG is less likely to be displaced outside the base, so the object is more stable
While the COM remains in the same place, the LOG moves within the wide base of support

Newton’s 1st Law of Linear Motion

Law of Inertia
Reluctance to change its state of rest or motion

Newton’s 2nd Law of Linear Motion

Law of acceleration
F = ma
If multiple forces, then F1 + F2 + … = ma
Free-body diagram

Newton’s 3rd Law of Linear Motion

Law of reaction
For every action, there is an equal and opposite reaction

Friction

Force due to relative contact (F = mu*N)
0 < mu < 1
Passive force resistance
Direction of friction: opposite from that of the motion/motion tendency
At some point, the pulling force will be great enough so that the friction force cannot prevent movement

Coefficient of friction

Coefficient of static friction [mu(s)] - the value given to represent the amount of friction present when an object is motionless
Coefficient of dynamic friction [mu(d)] - the value given to represent the amount of friction present when an object is in motion

Strategies for friction

Minimizing friction as a resistance: lubrication like synovial fluid, tire inflation, skating, skiing, swimming
Maximize friction as a source of propulsion (cleats, pushoff in skating)

Momentum

Quantity of motion of a body
M = mv
Capacity to give impact
How hard it is to stop an object
Vector
Unit: kg*m/s

Conservation of momentum

Principle of conservation of momentum: In the absence of external forces, the total momentum of a given system remains constant
M(before) = M(after)
M(before, player 1) = m(1)*v(1)
M(before, player 2) = m(2)*v(2)
M(after, player 1 and 2) = [m(1) + m(2)]v(f)
m(1)v(1) + m(2)v(2) = [m(1) + m(2)]v(f)

Impact

Collision and exchange of force during short time interval
Coefficient of restitution (e): determines the elasticity of an impact; a measure of the springiness of collisions between two surfaces
e = velocity after impact/velocity before impact

Elasticity

Ability to regain original shape after collision/deformation
Types: elastic (e = 1), inelastic (0 < e < 1), plastic (e = 0)

Work

Accumulated effect of force over displacement
W = Fd
Scalar
Unit: Joule (J) = Nm
“+” = positive work (both force and displacement in same direction
“-” = negative work (force and displacement in opposite direction)

Mechanical power

Rate and intensity of work
P = F*v
Scalar
Unit: W (Watt) = J/s

Mechanical energy

Capacity to do mechanical work
Kinetic energy: due to motion
KE = 1/2mv²
Potential energy: due to position
PE = mgh
Strain energy: due to deformation
ME = KE + PE
Units: Joules

Mechanical energy conservation

If gravity is the only external force, ME = KE + PE = constant

Work-energy relationship in mechanical energy

W = change in KE + change in PE
Unit: Joules (J)