Fundamentals of motion

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14 Νοε 2013 (πριν από 3 χρόνια και 9 μήνες)

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Fundamentals of motion

Kinematics


Is the study of motion


The how, not the why



An object’s
position

means…



The location of object in space

How do we know if something
moves?

FRAME OF REFERENCE

RELATIVE MOTION

Frame of reference


An object or place used for comparison to
the main subject.


Reference Point


You get to pick what your measuring the
position of the object against



You get to pick positive and negative
direction

What is the most common reference
point?




Earth, ground or something attached to it

Reference



Reference point or
Frame of Reference

-
what is used to
determine motion of
an object



Standard frame of
reference is the solid
Earth

Relative motion




How fast is that car
moving on the highway?



If moving in the opposite
direction,
add

the
velocities of each object



If moving in same
direction,
subtract

the
velocities of each

SCALAR VS VECTOR VALUES

Comparison

Vector Values


Any vector value must
indicate:


a magnitude


a direction for the value


a unit of measure



Magnitude means the size



Ex:
-
12.3 m/s



(
-
) indicate direction



12.3 indicates size



m/s are the units



Scalar Values


Only indicate magnitude
and units

VALUES OF MOTION

What values are measured
about the motion of an object?

Can you think of 3?

Values of Motion


How Far?



How Fast?



Is the motion unchanging?

DISTANCE AND
DISPLACEMENT

The measurement of how far


Measures the length that someone moves



Measured in meters (m)




Two ways that this can be accomplished



Use the same symbol for representation of
length measurement: d





Displacement and Distance


Displacement



Length of straight line
between initial and
final position



Direction matters


Distance



Length of the path
followed between
start and final position



Direction does not
matter

Distance




Measures the length
of the path taken by
an object from one
point to the next



Standard unit of
measure is meters

Displacement




Measurement of the
straight line length
between start position
and final position



Standard units are
measured in meters



Direction does matter

Similarities




Both measure length and use same units

Can you think of an example
when an object’s distance
value is the same as its
displacement?

Your car has to travel a displacement
of 5 meters (twice)


That means the length between your start
position and final position has to be
greater than 5 meters



To determine displacement, use a tape
measure, count blocks on the hallway floor
or use string

Identifying start and final position for
your vehicle


Start position:


Point where left front wheel touches the
ground




Final Position:


Point where left front wheel touches the
ground

SCALAR AND VECTOR
VALUES

Types of measurement


Velocity



Displacement/time



Direction matters



Units are m/s


Speed



Distance/time



Direction is not
indicated



Units are m/s

SPEED AND VELOCITY

Measure the rate of motion


How fast an object travels



Determined by how far it travels over an
amount of time



Rate (fraction)

Speed, velocity


Speed is distance / time


Velocity is displacement / time



Velocity will indicate a direction



Both measure rate of motion (how fast)
and use same units

Speed




A rate of motion
which


How much distance
traveled in an amount
of time


Standard units are
m/s

Velocity


Also a rate of motion


Change of position (displacement) over
time


Same units



Direction does matter

Difference between velocity and
speed


Speed is calculated using distance


Velocity uses displacement



Therefore the velocity value should
indicate a direction

Average speed, velocity



Are rates of motion calculated over a time
period



Velocity = overall displacement / time


Speed = overall distance / time

Average Speed


Speed found by taking the overall distance
divided by the overall time



Rate of motion over a period of time



Not at any single point in time

Measurement of speed


Average velocity = displacement / time



Average speed = distance / time



Symbol in the book will be same = v



Equation

v = d / t

Constant speed


Rate of motion does not change over a
period of time




Cruise control


Desktop computers

Constant speed, velocity





Occurs when the rate of motion does
NOT

change

Instantaneous speed

Rate of motion at a single point in time


Harder to calculate than average speed

Difference between average and
instantaneous speed



Average
: measured over some amount of
time


Instantaneous
: at one moment of time

Instantaneous Velocity

-
vs
-

Average velocity




Instantaneous means at one infinitesimally
small point in time


Find by measuring the slope of the tangent line


Average means over a measurable block
of time


Find by calculation

Resultant velocity


Finding the overall velocity of an object given a
specific frame of reference by combining rates of
motion




Person on bus compared to earth


Person in airplane compared to earth

Average, Instantaneous,
Constant, Resultant are words
that can be used describe
speed
or velocity

Meanings are the same

How to calculate average velocity










V = d







t