Test Notes for Physics 2210
Useful Constants
Table of useful constants
Name
Symbol
Speed of Light in Vacuum
c
2.99792458 x 108 m/s
Magnitude of electron
charge
e
1.602176634 x 10-19 C
Gravitational Constant
G
6.6740831 x 10-11 N m2/kg2
Planck's Constant
h
6.62607015 x 10-34 J s
Boltzmann Constant
k
1.380649 x 10-23 J/K
Avogadro's Number
NA
6.02214076 x 1023 mol-1
Ideal Gas Constant
R
8.314462618 J/(mol K)
Mass of Electron
me
9.10938356 x 10-31 kg
Mass of Proton
mp
1.672621898 x 10-27 kg
Mass of Neutron
mn
1.674927471 x 10-27 kg
Magnetic Permeability
Constant
μ0
4π x 10-7 Wb / (A m)
Electric Permittivity
Constant
ε0
8.854187817 x 10-12 C2 / (N m2)
Coulomb Constant
Value
k = (4π ε0)-1 8.987551787 x 109 N m2 / C2
Unit Conversion Factors
Length
Speed and Acceleration
1 m/s = 3.281 ft/s
1 km = 0.6214 mi
1 mph = 1.466 ft/s
1 m = 3.281 ft = 39.37 in
1 light-year = 9.461 x 1015 m
Mass
1 u = 1.661 x 10-27 kg
1 kg = 2.205 lbs of force
(at sea level on earth)
Volume
Angle
1 m3 = 1000 liter (L)
1 rad = 57.30° = 180° / π
1 m3 = 35.31 ft3
1 revolution = 360° = 2π rad
1 gallon = 3.788 liters
1 rev/min (rpm) = 0.1047 rad/s
1 mph = 1.609 km/h
1 m/s2 = 3.281 ft/s2
Force
Pressure
Energy and Power
1 cal = 4.186 J
1 N = 0.2248 lbs
1 atm = 101,300 Pa = 14.7 psi
1 Btu = 1055 J = 252 cal
1 mmHg = 133.3 Pa
1 hp = 746 W
Metric Prefixes
Prefix
Power of ten
Prefix
Power of ten
Prefix
Power of ten
pico
p
10-12
milli
m
10-3
mega
M
106
nano
n
10-9
centi
c
10-2
giga
G
109
micro
μ
10-6
kilo
k
103
tera
T
1012
Useful Mathematical Relations
Quadratic Formula:
Geometry:
Chapter 1: Units, Physical Quantities, and Vectors
Vector Magnitude and Direction
The angle θ is defined to be measured counter-clockwise from the positive x axis.
Be careful computing the direction of any vector from inverse tangent.
Vector Addition and Multiplication
Products of Vectors
The Dot Product: For two vectors,
The Cross Product: For two vectors,
and
and
, and the angle between
, and the angle between
and
and
defined by ϕ, the dot product
defined by ϕ, the cross product
is:
is:
Chapter 2: Motion Along a Straight Line
Understanding Change: For quantity Q, the change in the quantity is: ΔQ = Q2 - Q1.
Average Velocity, Instantaneous Velocity, and Acceleration Along a Single Dimension x
Motion with Constant Acceleration
Velocity and Position by Integration
Free Fall
Chapter 3: Motion in Two or Three Dimensions
Position, Velocity, and Acceleration Vectors
Projectile Motion
Uniform Circular Motion
Chapter 4: Newton's Laws of Motion
Forces in Equilibrium
Newton's Second Law
Newton's Third Law
Mass and Weight
Chapter 5: Applying Newton's Laws
Tilted Axes
For a vector pointed above a slope at the angle α from the tilted positive x-axis,
Friction
Fluid Resistance and Terminal Speed
Dynamics of Circular Motion
= Ax = A cos(α) and
= Ay = A sin(α)
Chapter 6: Work and Kinetic Energy
Work
Work - Energy Theorem
Power
Chapter 7: Potential Energy and Energy Conservation
Gravitational Potential Energy
Elastic Potential Energy
Conservation of Energy
Force and Potential Energy
Chapter 8: Momentum, Impulse, and Collisions
Momentum and Impulse
Conservation of Momentum
Elastic Collision - Special Case
Chapter 9: Rotation of Rigid Bodies
Angular Velocity and Acceleration
Motion with Constant Angular Acceleration
Links between Linear and Angular Motion
Moment of Inertia
Rotational Kinetic Energy
Moments of Inertia of Various Bodies
Parallel-Axis Theorem
Chapter 10: Dynamics of Rotational Motion
Torque (Moment)
Combined Translation and Rotation
Work and Power in Rotational Motion
Angular Momentum
Chapter 11: Equilibrium
Two Conditions for Equilibrium
Center of Gravity
Chapter 12: Fluid Mechanics
Density
Pressure with Depth in a Fluid
Hydraulics (Pascal's Law)
Buoyancy
Fluid Flow
Chapter 17: Temperature and Heat
Temperature Scales
Heat and Calorimetry
Chapter 18: Thermal Properties of Matter
Ideal Gases
Heat Capacities
Chapter 19: The First Law of Thermodynamics
Work and Energy for Ideal Gas Processes
First Law of Thermodynamics
Thermodynamic Processes
Heat Capacities of an Ideal Gas
Adiabatic Processes for an Ideal Gas