Biomechanics Exam 1 SDSU

1 in \= \_____ cm

2.54 cm

1 mile \= \____ km \= \____ m

1.609 km, 1609 m

Proximal

In proximity to or closer to. Generally meaning closer to the torso.

Distal

Distant or further away. Generally meaning further from the torso.

Sagital

Divides into right and left halves

Frontal

Divides into front and back halves

Transverse

Divides into top and bottom halves

Movement occurs in the plane that it is \____ to.

Parallel

What type of exercises occur in the sagittal plane?

Situps
Back extensions
Bicep curls
Running

What type of exercises occur in the frontal plane?

Jumping jacks
Side bends
Lateral dumbbell raises

What type of exercise occurs in the transverse plane?

Anything that involves rotation

What type of motion occurs in the sagittal plane?

Flexion/Extension

What type of motion occurs in the frontal plane

Adduction/Abduction, side flexion, inversion/eversion

What type of motion occurs in the transverse plane

internal/external rotation, horizontal flexion/extension, and supination/protination

What axis of motion corresponds with the sagittal plane?

Mediolateral Axis

What axis of motion corresponds with the transverse plane?

Superior-inferior Axis

What axis of motion corresponds with the frontal plane?

Anterior-Posterior Axis

What kind of activities are primarily planar?

Running, cycling, cartwheeling, and a softball pitch

What kind of activities are multiplanar?

Tennis serve, baseball pitch, and roundhouse kick

The mass of an object is determined by the amount of \_________ in the object, and is measured in \___.

matter, kg

What 2 things does mass determine?

1. Measure of inertia
2. Determines the strength of gravitational attraction

Weight is a \________ and is measured in \____. The equation for weight is \______________.

force, N
Fg\=W\=mg

1 lb \= \____ kg

0.455 kg

An object's \______ is the same everywhere, whereas it's \______ changes depending on where it is (eg. moon vs earth).

mass, weight

Mechanics

Analysis of the motion of an object and the forces acting upon the object

Biomechanics

Application of principles of mechanics to the study of living organisms

What are the two main subfields of biomechanics?

Rigid Body Biomechanics
Deformable Body Biomechanics

What are the two main divisions within Rigid Body Biomechanics?

Statics
Dynamics

Statics

The study of systems in a state of equilibrium (at rest or in a constant state of motion)

Forces are balanced \= equilibrium

Dynamics

Interested in changing systems
Broken down into two major areas: Kinematics and Kinetics

What are the two main divisions within Dynamics?

Kinematics
Kinetics

Kinematics

The study of motion WITHOUT consideration of the CAUSE eg. speed

Describing and measuring human movement by focusing on the type of motion, the direction, and the quantity of the motion without regard for the forces that may produce that movement

Kinetics

The study of the CAUSE of motion (forces) eg. muscle force

Deals with forces that produce, stop, or modify motion of bodies as a whole or of individual body segments

Reference Frames (Cartesian Coordinates)

System describing a body's location in space (aka coordinate system)
1. Direction (3 axes)
2. Location (point of origin)
Follows right hand rule (pointer finger x, middle y, thumb z)

Right Hand Rule

(pointer finger x, middle y, thumb z)

An angle CCW from the x-axis is \_____. An angle CW from the x-axis is \_____.

positive, negative

Vector

Fully described by both magnitude and direction (how big and what is direction)

Displacement
Velocity
Acceleration
Force

Tip to Tail Method

Method of vector addition where one can add any two vectors by placing the tail of one so that it meets the tip of the other one

Vector Specified Two Ways:

Directly: magnitude and direction (A and theta)

Indirectly: X and Y components (xA and yA)

REMEMBER on Vectors

Magnitude sign is ALWAYS POSITIVE

Direction sign depend on reference (components sign pos/neg based on how vectors points)

Scalar

Fully described by magnitude (how big)

Distance
Speed
Maass
Energy
Temperature

Vector Equality

Two vectors are considered equal if they possess the same magnitude and direction

Commutative law of addition

When vectors are added together, the sum is independent of the order of addition

Resultant

A vector that represents the sum of all individual vectors acting upon a system

What are the 7 steps of multiple-vector composition?

1. Draw vectors in coordinate system, with tails at the origin
2. Break them down: turn each vector into x and y components
3. Add up all the x's\= Rx
4. Add up all they y's\= Ry
5. Put them back together again: draw Rx and Ry from tip-to-tail and compose them into the final R
6. Use Pythagorean theorem to find magnitude (POSITIVE)
7. Use tan-1 to find direction (NEGATIVE OR POSITIVE)

Position (P)

Location in space

Use a vector to describe a body's position, P, in the frame of reference (magnitude + direction)

∆P \= "change in position" \= displacement
∆P \= P (final) - P (initial)

Displacement

Change in position of an object (in a specific direction i.e. 5 miles Northeast, or by X and Y components i.e. 4 miles E and 3 miles N)

Vector \> specify as magnitude in a specific direction

∆P \= "change in position" \= displacement
∆P \= P (final) - P (initial)

Distance

How far the object traveled to get from P (initial) to P (final)

Scalar \> actual route taken

T/F Distance is always greater than the magnitude of displacement

F

Rates

How fast something is changing

Rate of change \= ∆ something / ∆ t

Ie. Units \= liters/min or m/s

Velocity

Rate of change of position (displacement/time)
Vector
\[m/s]

Vavg \= ∆P /∆t
∆P \= displacement P(final)-P(initial)
∆t \= change in time t(final)-t(initial)

Speed

Rate of change of distance
Scalar \> only informs how fast, no direction
m/s

Savg \= d/∆t

SPEED and VELOCITY are NOT THE SAME

Acceleration

Rate of change of velocity
Vector
\[m/s2]

Aavg \= ∆V / ∆t
∆V \= V(final) - V(initial)

Acceleration directiions

Positive acceleration (+ direction)
∆V is pos, V value is increasing so f \> i

Negative acceleration (- direction)
∆V is neg, V value is decreasing so f < i

If the V value increases, then acceleration is \_________. If the V value decreases, then acceleration is \_________.

positive, negative

tangent

A line in the plane of a circle that intersects the circle in exactly one point.

Distinguish between average and instantaneous rates

Slope between two time points gives average rate
Slope at a time point gives instantaneous rate

Instantaneous speed/velocity

The rate of motion at a given instant in time (delta t becomes very small)

T/F with a linear velocity, Vavg \= Vinstantaneous

T

Acceleration

slope of the time-velocity curve

Velocity

slope of the time-position curve

Change in position

area under the time-velocity curve

Change in velocity

area under the time-acceleration curve

Constant acceleration (flat slope) results in a \________ change in velocity.

linear (velocity changes at a constant rate)

Constant velocity (flat slope) results in a \________ change in displacement.

linear (displacement changes at a constant rate)

A linear change in velocity results in a \_______ change in displacement.

non-linear (slope is not constant)

Uniform acceleration (eg. gravity) can predict \__________ and \____________.

displacement, velocity

Slope

Rise over run

∆ vertical value / ∆ horizontal value

Projectile

A body in free fall that is subject only to the forces of gravity and air resistance (neglected)

Why do we analyze the horizontal and vertical components of projectile motion independently?

The vertical component is influenced by gravity, the horizontal component is not

Vertical projectile motion relies on:

Constant (yA \= -9.81 m/s)
Symmetry (when appropriate)

Symmetry in upward projectiles

patter of change in vertical position of a projectile is SYMMETRICAL ABOUT THE PEAK

for symmetry need initial positive yVi (moving up)

Projectile trajectory

Motion in both x and y directions
Parabolic shape (curved, symmetrical)
Influenced by initial projection speed, projection angle,
and relative projection height

What does the shape of a trajectory depend on?

Projection angle

Initial conditions determine motion that a projectile will have:

TRAJECTORY:
Projection speed \> size
Projection angle \> shape
Relative projection heigh \> location

If want to max time of flight or heigh reached:

Increase projection angle
Increase projection speed
Higher release (projection height)

If want to minimize time of flight:

Decrease projection angle
Increase projection speed

If want to max horizontal displacement:

Projection angle should approach 45 degree
Increase projection speed
Higher release (projection) height

Categories of Forces

Every force has one property from each category:

PUSH or PULL forces
CONTACT or NON-CONTACT forces
EXTERNAL or INTERNAL forces

ie. Gravity: pull, non-contact, external
People: push, contact, external

Internal forces

Act completely within defined system

Can cause the object to change shape but cannot produce any changes to body's COM without an external force

Something INSIDE system applies a force to something else INSIDE system

External forces

Act on the system from the outside

Causes changes to a body's motion

Something OUTSIDE system applies a force to something INSIDE system

Free Body Diagram (FBD)

Diagram showing vector representations of all the external forces acting on a defined system

1. First law of uniformly accelerated motion (vertical velocity)
2. Second law of uniformly accelerated motion (vertical position)
3. Third law of uniformly accelerated motion (vertical velocity)

1. yVf \= yVi + (ya)(tf)
2. Yf \= Yi + (yVi)(tf) + (1/2)(ya)(tf2)
3.yVf2 \= yVi2 + (2)(ya)(∆ Y)

The horizontal \_______ of a projectile is constant. Therefore, \___________ is zero.

velocity, acceleration

3 Equations for the horizontal motion of a projectile (uniform velocity)

1. Xf \= Xi + (xVavg)(∆t)
2. xVf \= xVi \= Constant
3. a \= 0

3 things projectile trajectory is it influenced by?

Initial speed
Projection angle
Relative projection height

What are the 7 steps of the problem solving strategy for projectiles?

1. Write down which variable you need to know
2. List all known variables
3. Break up initial velocity into horizontal and vertical components
4. Figure out which equations allow you to solve for the unknown variable from the known variables
5. Rearrange the equation to isolate the desired variable
6. Plug in the known variables
7. solve.

Trajectory shape depends only on projection \_________.

angle

Relative projection height \= ?

Relative projection height \= (projection height) - (landing height)

Contact forces vs. Non contact forces

CONTACT forces: between objects touching each other

NON CONTACT forces: eg. gravitational force

Equation for the force of gravity (weight)

W \= Fg \= mg

If only given initial velocity, which direction do you analyze to determine the time of flight of a projectile?

Vertical

Net force

The vector addition of all the external forces acting on an object

Inertia

A resistance an object has to change in motion, specifically a resistance to change in a body's velocity; resist acceleration

Applies to bodies at rest, moving linearly, and rotating

Quantitively measured by an object's MASS (units kg)

- Has mass then has inertia

Mass is \____________ related to resistance to change in motion (Inertia).

directly

Momentum definition and equation

The quantity of motion that an object possesses
- relates to effort needed to stop a motion

An objects linear momentum is related to its mass (m) and
Linear Velocity (V)

L \= mV

Still object (V \= 0 ) has no momentum

Newton's first law is the law of \___________, the second is the law of \__________, and the third is the law of \___________.

inertia, acceleration, reaction

Newtons 1st law

"The Law of Inertia"

An object at rest stays at rest and an object in motion stays in motion with the same velocity unless acted upon by an unbalanced force

Conservation of momentum

- ie. drinking coffee while sitting in a moving car
- ie. horizontal motion of a projectile

Newtons 1st Law: Conservation of Momentum

Formula: L \= mV

If ΣF \= 0 then L constant, mV constant
∆L \= 0, ∆ (mV) \= 0

Still object (V \= 0 ) has no momentum

Newton's 2nd law

"The Law of Acceleration"

The acceleration of an object is directly proportional to the net force exerted on it (and inversely proportional to its mass)

ΣF \= mA