Mechanical work

equal to the product of the magnitude of a force applied against an
object and the distance the object moves in the direction of the force
W=F*d
Joules=Newton-meters

To determine the amount of work done on an object we need to know:

the average force exerted on the object the direction
of the force the displacement of the object along the line
of action of the force during the time the force acts on the
object

Positive work

done by a force acting on an object if the object is displaced in the
same direction as the force
Ex: throwing a baseball, lifting a weight, jumping off the ground

Negative work

done by a force acting on an object when the object is displaced in
the direction opposite the force acting on it
Ex: catching a ball, lowering a weight, landing a dismount

Power

how much work is done in a specific amount of time
P=W/t --> P=F(d)/t
P=F*v
Watts= J/s

Human body movement involves

angular displacement being performed by joints

Displacement can be

linear or angular
angular movements: P=torque*angular velocity

Peak power

also referred to as instantaneous power
highest power value achieved during the movement being observed

Average power

the product of the average force and the average velocity of an
entire movement

Internal power

product of joint torque and angular velocity torque or
angular velocity may dominate in producing the highest power
values balance between these may change through a joint
ROM

External power

aggregate of multiple joint powers resulting in a body movement
Ex: vertical jump is a common method to analyze whole body power

Maximize power

lower intensity loads (velocity) higher intensity
loads (Force) mixed methods(force and velocity)

To increase power output

overall strength must be maximized rate of force
development important to develop ability to generate high
forces as velocity of shortening increases; optimum load

Maximization of overall strength levels results in

significant improvements in muscular power
training should establish adequate strength, this should be
acquired prior to incorporating activities targeting power development

Rate force development is determined from

slope of the force vs time curve
RFD=delta force/delta time

as a muscles velocity of contraction increases

its maximum force of contraction decreases
INVERSE RELATIONSHIP between force and velocity

maximum power output of the muscle occurs at

a velocity approximately one-half the muscle's maximum contraction velocity

Energy

capacity to do work

Kinetic energy

energy due to motion
KE=1/2mv^2

Potential energy

energy due to position
gravitational potential energy Strain energy

Gravitational Potential energy

related to the object's weight and its elevation or height above the
ground or some reference
PE=mgh

Strain energy

related to the objects stiffness, material properties, and its deformation
greater the deformation--> greater strain energy
SE=1/2k*(delta)x^2
delta x=change in length
k=stiffness or spring constant of material

Kinematics

describes motion
can be qualitative or quantitative

Pythagorean Theorem

A^2+B^2=C^2

Sin (theta)

opposite/hypotenuse

cos (theta)

adjacent/hypotenuse

tan (theta)

opposite/adjacent

linear kinematics

the branch of dynamics concerned with the description of motion

Motion

the action or process of a change in position

Linear motion

referred to as translation
occurs when all points on a body or object move the same
distance, in the same direction, and at the same time
Rectilinear translation, curvilinear translation

rectilinear translation/motion

occurs when all points on a body or object move in a straight line so
the direction of motion does not change, the orientation of the object
does not change, and all points on the object move the same distance

Curvilinear translation/motion

occurs when all points on a body or object move so that the
orientation of the object does not change and all points on the object
move the same distance
paths are curved so direction of motion is constantly changing

Angular motion

rotary motion or rotation
occurs when all points on a body or object move in circles about
the same fixed central line or axis
can occur about an axis within the body or outside the body

position

location in space

distance

scalar quantity (magnitude)

displacement

vector quantity (magnitude and direction)
straight-line distance in a specific direction from initial to
final position

speed

rate of motion
scalar quantity
speed=distance/time

velocity

rate of motion in a specific direction
vector quantity
v=displacement/time
if motion is positive so is velocity.. same for negative

acceleration

rate of change in velocity, or the change in velocity occurring over
a giver time interval
a=delta V/ delta T
=0 when velocity is constant

angular distance

sum of all angular changes undergone by a rotating body

angular displacement

the different in the initial and final positions of the moving body
defined by magnitude and direction
clockwise is negative, counterclockwise is positive

radian conversion

57.3 degrees

revolutions

degrees/360=revolutions

angular speed

angular distance covered divided by the time interval or which the
motion occurred
scalar quantity
? = ?/?t
(angular speed=angular distance/change in time)

angular velocity

change in angular displacement that occurs during a given period of time
vector quantity
? = ?/?t
(angular velocity=angular displacement/change in time)

angular acceleration

rate of change in angular velocity
vector quantity
? = ? ? /?t
(angular acceleration=change in angular velocity/change in time)

the greater the radius is between a point on a rotating body and the
axis of rotation

the greater the linear distance undergone by that point during an
angular motion
S = r?
(linear distance=radius*angular distance)

the greater the radius is between a point on a rotating body and the
axis of rotation

the greater the linear velocity undergone by that point during an
angular velocity
V = r ?
(linear velocity=radius*angular velocity)
angular velocity must be in rad/s

Newton's first law

Law of Inertia: a body will maintain a state of rest or constant
velocity unless acted upon by an external force that changes the state

Inertia

property of an object that causes it to remain in a state of either
rest or motion
amount of fore needed to alter the object's velocity is directly
related to the amount of inertia it has
the measure of linear inertia in a body is its mass

Newton's second law

Law of Acceleration: a force applied to a body causes an acceleration
of that body of a magnitude proportional to the force, in the
direction of the force, and inversely proportional to the body's mass

Newton's second law formula

Force=mass*acceleration

Impulse

product of force and the time over which the force is applied
equal to the area under the force-time curve

impulse during gait

objective is to apply the largest force for the longest possible time
greater the impulse the greater the change in momentum
optimized by: minimizing breaking impulse, maximizing propulsive impulse

maximizing propulsive impulse

improve hip extension(force and ROM) to lengthen the propulsive
impulse, increases the force and the time over which the force is applied

momentum

greater the impulse, greater the change in momentum
product of mass and velocity
L=mv
(linear momentum=mass*instantaneous v)

according to newton's first law: if the net force acting on the
object is 0 then

the velocity of an object is constant and therefore its momentum is constant

Newton's third law

Law of Reaction: for every action, there is an equal and opposite reaction
Ex: 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

Elastic Collision

when two objects collide in a head-on collision, their combined
momentum is conserved

Inelastic Collisions

Momentum is conserved after the collision, but instead of bouncing
off each other, the objects in the collsion stay together after the
collision and move with the same velocity
(m1)(u1)+(m2)(u2)=(m1+m2)(v)

Linear inertia

the property of an object to resist changes in its linear motion
dependent only to the mass of the object(larger mass --> more inertia)

Angular inertia(moment of inertia)

property of an object to resist changes in its angular motion
dependent on the mass and the distribution of the mass
�I = ? mi ri2 (about center of gravity)

Angular inertia about eccentric axes

if an object rotates about a fixed axis that does not pass through
the center of gravity
?I = Icg + mr^2

radius of gyration

represents the object's mass distribution with respect to a given
axis of rotation

greater the angular inertia...

the harder it is to change an object's motion

Centripetal force

prevents rotating body from leaving its circular path
direction is always towards center of rotation
speed of rotation is the most influential factor on magnitude of
centripetal force

Centrifugal force

an outward pulling force that opposes centripetal force

Both air and water are fluid mediums that

exert forces on bodies moving through them
some mediums slow movement while others provide support or propulsion

Fluid

any substance that tends to flow or continuously deform when acted on
by a shear force

Relative velocity

the velocity of a body with respect to the velocity of something
else, such as the surrounding fluid
subtraction of the velocity of the fluid from the velocity of the body

fluid forces

forces produced by gases or liquids
buoyancy drag lift

the magnitude of the forces a fluid generates is impacted by the
properties of the fluid

density: ratio of mass/volume
specific weight: ratio of weight/volume
viscosity: resistance to fluid flow

fluid properties are influenced by fluid temperature and atmospheric pressure

more mass concentrated in a given unit of fluid volume at high
atmospheric pressures and lower temperatures

buoyancy

if an object exists in a fluid there is a force applied to the object
opposite gravity, the magnitude of the force is equal to the weight of
the fluid that the object displaces
Buoyancy=displaced volume*specific weight of fluid

buoyancy forces

line of force is applied opposite gravity and passes through the
"center of volume"
the heavier the amount of fluid displaced the greater the buoyant force

center of volume

the point around which a body's volume is equally distributed in all directions

drag

the resistance for forward motion of an object through a fluid
the result of fluid pressure on the leading edge of the object and
the amount of turbulence

turbulence

backward pull on the trailing edge
produces a suction force pulling the object in the opposite
direction of its intended path

Factors affecting drag

viscosity: thicker fluid, more drag
cross sectional area: greater CSA, greater drag
velocity: velocity doubles, drag force squared

Form drag

the shape of the object makes the fluid unable to follow the contours
of the object causing turbulence

Surface drag

friction that exists between the boundary layer and the object
boundary layer: the layer of fluid directly next to the object

laminar flow

smooth, unbroken fluid flow
can decrease surface drag and enhance laminar flow by shaving,
high-tech fabrics, etc.

lift

force generated by the changes in fluid pressure as the result of
different fluid velocities

bernoulli's principle

pressure in a moving fluid decreases as speed increases
faster the fluid flows, less pressure generated
differences on either side of an object may generate a lift force