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