Introduction to Kinematics

Dimensional Analysis

Measurement

  • measurement is
    limited by the accuracy
    of the equipment we use
  • you are allowed to
    approximate within 0.5 of
    the said unit
  • motion is relative

Mechanics

SI System

  • "system de' Internationale (1799),
    french revolution

Prefixes

Units

Base Units
(& dimensions)

Temperature (kelvin)

electric current (A)

Amount (mol)

Length (1m)

Mass (1kg)

Quadrant/10^7

Time (1s)

Platinum Iridium
Cylinder

Luminosity (cd)

9 192 631 700
Cesium 133 cycles

Derived Units

Constants

Avogadro's Constant

Boltzmann's Constant

Kb = 1.38 * 10^-23 J/K

  • (Joules of Ke)

Na = 6.022 * 10^23

Area (m^2)

Velocity (m/s)

Density (kg/l)

Acceleration (m/s^2)

Gravitational Acceleration

g = 9.8 m/s^2

(T)etra(10^12)

(G)iga(10^9)

(M)ega(10^6)

(u)mikro(10^-6)

(n)ano(10^-9)

(p)ico (10^-12)

Significant Figures

Operations
Round after all of a particular
operation is complete, not after
every operation.

Counting SigFigs

  • leading zeroes don't count
  • ending zeroes only count between/after the decimal
  • middle zeroes always count
  • digits 1-9 always count

Addition/Subtraction

  • round output by decimals

Multiplication/Division

  • round output by sigfigs

Applications

Strategy

  • you know all possible dimensions
    but would like to reduce variable load
    for an experiment.
  • You want to check the validity of an
    equation via dimensional analysis.
    An equation which passes dimensional analysis
    may or may not be correct, but an equation
    which fails dimensional analysis is definitely
    wrong.
  • 1) Replace all units with dimensions
  • 2) Set powers of dimensions equal
  • 3) Solve & then plug in

Diagrams

Vectors

  • force
  • derivatives of
    displacement

Kinematic Measurements

  • motion

Velocity (v)

Acceleration
"add celerity"


Displacement
(s)patium

Jerk

  • snap
  • crackle
  • pop

Mortons Law: vbar=(vf+vi)/2 (v is linear)
vf=vi+at (a is constant)**
{{instantaneous velocity}}

d=(vf^2-vi^2)/2a (a is constant)
d=vi(t)+(at^2)/2 {a is constant)

abar=(vf-vi)/(tf-ti)
{{instantaneous Acceleration}}

Amplitude

Magnitude

Derivative = step up

Integral = step down

Scalars

Dynamics

  • motion
  • force

Statics

  • motion
  • force
  • energy

Subdivisions

Force
an interaction which
causes change to
motion, shape. or
energy

Energy
An environments ability
to do work.
(work is done when
a force causes a change
in energy)

Motion
change in position

Oscilatory

Rotational

Random

Translational