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PHYS 2300 and 2305: General Physics I and II Formulas
Chapter 1 Chapter 2
Trig Formulas
sin 𝜃 =
Opposite
Hypotenuse
𝜃 = sin
− 1
Opposite
Hypotenuse
cos 𝜃 =
Adjacent
Hypotenuse
𝜃 = cos
− 1
Adjacent
Hypotenuse
tan 𝜃 =
Oppostie
Adjacent
𝜃 = tan
− 1
Oppostie
Adjacent
2
2
2
Velocity
Average Velocity
Average Speed
𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑠𝑝𝑒𝑒𝑑 =
Instantaneous Velocity
𝑣 = lim
∆𝑡→ 0
Vectors
Vector Addition by
Components
Where
𝑥
𝑥
𝑥
𝑦
𝑦
𝑦
Then to find 𝐶
use
2
2
2
Acceleration
Average Acceleration
Instantaneous
Acceleration
𝑎 = lim
∆𝑡→ 0
Motion of a particle with constant acceleration
0
1
2
0
𝑡 or 𝑑 =
1
2
0
0
1
2
2
Or 𝑑 = 𝑣
0
1
2
2
2
0
2
+ 2 𝑎𝑥 or 𝑣
2
0
2
Chapter 3 Chapter 4
Average Velocity/Acceleration
Average Velocity
Average Acceleration
Projectile Motion
X direction Y direction
𝑥
0 𝑥
𝑥
𝑦
0 𝑦
𝑦
𝑦
0 𝑦
0 𝑥
𝑥
or 𝑑 =
1
2
0 𝑥
𝑥
0 𝑦
𝑦
or ℎ =
1
2
0 𝑦
𝑦
0 𝑥
1
2
𝑥
2
or 𝑑 = 𝑣
0 𝑥
1
2
𝑥
2
0 𝑦
𝑦
2
or ℎ = 𝑣
0 𝑦
1
2
2
𝑥
2
𝑜𝑥
2
𝑥
or 𝑣
𝑥
2
𝑜𝑥
2
𝑥
𝑦
2
𝑜𝑦
2
𝑦
or 𝑣
𝑦
2
𝑜𝑦
2
Relative Motion 𝑣
𝐴𝐶
𝐴𝐵
𝐵𝐶
𝐴𝐵
𝐵𝐴
Newton’s Second Law
General
Component form
𝑥
𝑥
𝑦
𝑦
Gravitational Force
Gravitational Force
1
2
2
Weight
W=mg
Where 𝑔 = 𝐺
𝑚
1
𝑟
2
G=Universal Gravitational Constant = 6. 67 𝑥 10
− 11
2
2
Friction
Static Friction
(maximum)
𝑠
𝑚𝑎𝑥
𝑠
𝑁
Kinetic Frictional 𝑓
𝑘
𝑘
𝑁
Chapter 7 Chapter 8
Impulse and Momentum
Impulse 𝐽 = 𝐹
Linear Momentum, p p=mv 7.
Impulse-Momentum
Theorem
𝑓
0
Or J=Δp
Collision
Final Velocity of 2
objects in a head-on
collision where one
object is initially at rest
1: moving object
2: object at rest
𝑓 1
1
2
1
2
01
𝑓 2
1
1
2
01
Conservation of Linear
Momentum (in 1D)
0
𝑓
0
𝑓
0
Elastic Collision 𝑚 1
01
2
02
1
𝑓 1
2
𝑓 2
7.7b
Inelastic Collision
1
01
2
02
1
2
𝑓
Conservation of Linear
Momentum (in 2D)
1
01 𝑥
2
02 𝑥
1
𝑓 1 𝑥
2
𝑓 2 𝑥
1
01 𝑦
2
02 𝑦
1
𝑓 1 𝑦
2
𝑓 2 𝑦
Center of Mass
Center of mass
location 𝑥 𝑐𝑚
1
1
2
2
1
2
Center of mass velocity
𝑐𝑚
1
1
2
2
1
2
Angular displacement
0
Average angular
velocity
Average angular
acceleration
Motion of a particle with constant acceleration
0
0
0
2
2
0
2
Relationship between
angular variables and
tangential variables (t
subscript)
𝑇
𝑇
When no slipping
𝑇
𝑇
Centripetal acceleration
𝑐
2
Chapter 9
Moments of Inertia I for various rigid objects of Mass M
Torque and Inertia
Torque 𝝉
When at Equilibrium ∑ 𝜏 = 0 9.
Moment of Inertia
2
Newton’s Second Law
for a rigid body
rotating about a Fixed
axis
Work, Energy
Rotational work 𝑊
𝑅
Rotational Kinetic
Energy
𝑅
2
Angular Momentum 𝐿 = 𝐼𝜔 9.
Center of Gravity 𝑥
𝑐𝑔
1
1
1
1
1
2
See reverse side for moments of Inertia I for various rigid objects of Mass M
Thin walled hollow cylinder or
hoop
2
Solid cylinder or disk
2
Thin rod, axis perpendicular to
rod and passing though center
2
Thin rod, axis perpendicular to rod and
passing though end
2
Solid Sphere, axis through
center
2
Solid Sphere, axis tangent to surface
2
Thin Walled spherical shell,
axis through center
2
Thin Rectangular sheet, axis along one
edge
2
Thin Rectangular sheet, axis parallel to sheet and passing
though center of the other edge
2
Chapter 11 Chapter 12
Density 𝜌 =
Pressure
Specific Gravity =
1. 000 × 10
3
3
Pressure and depth
in a static Fluid
P
1
is higher than P
2
2
1
Gauge Pressure
Archimedes’
principle
𝐵
𝑓𝑙𝑢𝑖𝑑
Mass Flow Rate
Volume flow rate
Bernoulli’s Equation
𝑃
1
1
2
𝜌𝑣
1
2
1
= 𝑃
2
1
2
𝜌𝑣
2
2
2
Equation of
continuity
1
1
1
2
2
2
equation of
continuity ( )
1
1
2
2
Force to move
Viscous Layer with
constant velocity
Poiseuille’s law
4
2
1
Force and Area if
Pressure same
1
1
2
2
2
1
2
1
Temperature Scales
Fahrenheit to
Celsius
Celsius to
Fahrenheit
Celsius to Kelvin
K=C+273.15 or 𝑇 =
𝑐
Thermal Expansion
Linear Thermal
Expansion
𝑜
Volume Thermal
Expansion
0
Heat and Power
Heat and temperature
change
Heat and phase change
% Relative Humidity
𝑤𝑎𝑡𝑒𝑟 𝑣𝑎𝑝𝑜𝑡
𝑤𝑎𝑡𝑒𝑟 𝑣𝑎𝑝𝑜𝑡
Chapter 13
Heat and Power
Power P=Q/t
Heat Conducted
Radiant energy
e emissivity
𝜎 = 5. 67 x
J/(s*m
2
*K
4
T temp in Kelvins
A surface area
4
Net radiant Power
T object Temp in kelvins
T
o
environment temp in
Kelvins
𝑛𝑒𝑡
4
0
4
Chapter 15
First Law of Thermodynamics
First Law Δ𝑈 = 𝑈 𝑓
0
Note:
∆𝑈 Change in Internal Energy
Q (heat) is positive when the system gains heat and negative when it loses
heat. W (work) is positive when work is done by the system and negative
when work is done on the system.
Monatomic Ideal Gas
Internal Energy
*R=8.31 J/(mol K)
Applications of First Law
Process
Work Done First Law
Isobaric
(constant pressure)
𝑓
𝑖
(Eq 15.2)
𝑓
𝑖
5
2
Isochoric
(constant volume)
W=0 J ∆𝑈 = 𝑄 − 0 𝐽
3
2
Isothermal
(constant temp)
𝑓
𝑖
(Eq. 15.3)
𝑓
𝑖
Adiabatic
(no heat flow)
𝑖
𝑓
𝑖
𝑓
Adiabatic
expansion/compression
of an ideal gas
0
0
𝛾
𝑓
𝑓
𝛾
Heat with known
number of moles
molar specific heat
𝑝
𝑣
Heat Engines
The efficiency e of a
heat engine
𝐻
𝑐
𝐻
Conservation of energy
requires
𝐻
𝑐
Carnot Engine
For a Carnot engine
𝐶
𝐻
𝐶
𝐻
Efficiency e for a
Carnot engine 𝑒
𝑐𝑎𝑟𝑛𝑜𝑡
𝐶
𝐻
Coefficient of Performance (COP )
COP of a refrigerator or
an air conditioner
𝑐
𝐻
𝐶
COP of a heat pump 𝐶𝑂𝑃 =
𝐻
Entropy
change in entropy Δ𝑆 = (
𝑅
change in entropy
𝒖𝒏𝒊𝒗𝒆𝒓𝒔𝒂𝒍
𝑢𝑛𝑖𝑣𝑒𝑟𝑠𝑎𝑙
𝑠𝑦𝑠𝑡𝑒𝑚
𝑠𝑢𝑟𝑟𝑜𝑢𝑛𝑑𝑖𝑛𝑔𝑠
𝑐𝑜𝑙𝑑
𝐻𝑜𝑡
Energy unavailable for
doing work
𝑢𝑛𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒
0
𝑢𝑛𝑖𝑣𝑒𝑟𝑠𝑒
Chapter 16
Waves
Speed of a Wavelength 𝑣 = 𝑓𝜆 =
Speed of a wave on a
string
description
+x direction
description
Speed of Sound
Speed of Sound in a
Gas
k= 1.38x
Speed of sound in a
liquid 𝑣 = √
𝑎𝑑
Speed of sound in solid
bar 𝑣 = √
Sound Intensity
Intensity 𝐼 =
Intensity - uniform in
all directions
2
Intensity level in
decibels
I0 =1x10-12W/m
𝛽 = ( 10 𝑑𝐵) log (
𝑜
Doppler Effect
Source Moving toward
stationary observer
𝑜
𝑠
𝑠
Source Moving away
from stationary
observer
𝑜
𝑠
𝑠
Observer moving
toward stationary
source
𝑜
𝑠
𝑜
Observer moving away
from stationary source
𝑜
𝑠
𝑜
Chapter 19 Chapter 20
Work and Electric
Potential Energy
𝐴𝐵
𝐴
𝐵
Electric Potential 𝑉 =
0
Electric Potential
Difference
Charge moves from A
to B
𝐴
𝐵
𝐵
0
𝐴
0
𝐴𝐵
0
Electric Potential
Difference
Charge moves from B
to A
𝐵
𝐴
𝐴𝐵
0
Total Energy
2
2
2
Electric field 𝐸 = −
19.7a
Charge on each plate
of a capacitor
Dielectric constant
(E’s are electric fields
without and with a
dielectric)
𝑜
Capacitance of a
parallel plate capacitor
0
Electric Potential
Energy Stored in a
capacitor
2
2
Energy Density Energy Density =
0
2
Current (if electric
current is constant)
Ohms Law
𝑉 = 𝐼𝑅 𝑜𝑟 𝑅 =
Resistance with length
L, cross-sectional area
A
Resistance and
Resistivity (T temp)
0
[ 1 + 𝛼
0
]
0
[ 1 + 𝛼
0
]
Electric Power
𝑃 = 𝐼𝑉, 𝑃 = 𝐼
2
2
AC Circuits
0
sin( 2 𝜋𝑓𝑡)
0
sin( 2 𝜋𝑓𝑡)
RMS Formulas with
Current and Voltage
𝑟𝑚𝑠
0
𝑟𝑚𝑠
0
Average Power
𝑟𝑚𝑠
𝑟𝑚𝑠
𝑟𝑚𝑠
2
𝑟𝑚𝑠
2
Series
(I is the same)
𝑠
1
2
3
𝑠
1
2
3
Parallel
(V is the same)
𝑠
1
2
3
𝑝
1
2
3
RC circuits
0
[ 1 − 𝑒
−𝑡
𝑅𝐶 ] (charging)
0
−𝑡
𝑅𝐶 (discharging)
Chapter 21 Chapter 22
Magnitude of magnetic
Field
𝜇
0
= 4 𝜋 × 10
− 7
𝑇 ∙ 𝑚/𝐴
0
|𝑣 sin 𝜃
0
0
0
Radius of circular path
of particle caused by F
Relationship between
Mass and B
2
2
2
Force on a current in a
magnetic field
Torque on a current-
carrying coil
𝜙 is the angle between direction of B
and the normal plane
Ampere’s Law ∑ 𝐵
||
0
RHR 1: Fingers point along the direction of 𝐵
and the thumb points along the
velocity 𝑣⃗ The palm of the hand then faces in the direction of 𝐹
that acts on a
positive charge.
RHR 2 : Curl the fingers of the right hand into a half-circle. Point the thumb in
the direction of the conventional current I, and the tips of the fingers will
point in the direction of 𝐵
Motional emf ℰ = 𝑣𝐵𝐿 22.
Magnetic Flux Φ = 𝐵𝐴𝑐𝑜𝑠𝜙
Faraday’s Law ℰ = −𝑁
Emf induced ion a
rotating planar coil
ℰ = 𝑁𝐴𝐵𝜔 sin(𝜔𝑡) = ℰ
0
sin(𝜔𝑡) 22.
Current 𝐼 =
Mutual Inductance
𝑠
𝑠
𝑝
Emf due to mutual
inductance
𝑠
𝑝
Self-Inductance 𝐿 =
Emf due to self-
inductance
𝑠
Energy stored in an
inductor
2
Energy Density 𝐸𝑛𝑒𝑟𝑔𝑦 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 =
0
2
Voltage and turns of
primary and secondary
coil
𝑠
𝑝
𝑠
𝑝
Current and turns of
primary and secondary
coil
𝑠
𝑝
𝑝
𝑠
Power Power=Energy*time
Chapter 25
Concave Mirror
Focal length Concave
mirror
Focal length Convex
Mirror
Mirror Equation
𝑜
𝑖
Magnification
Equation
𝑖
𝑜
𝑖
𝑜
Plain Mirror
Forms an upright virtual image
Image located same distance behind the mirror as the object in front
Heights of object and virtual image the same
Information for Spherical mirrors
Focal Length
Object distance
Image Distance
Magnification (sign)
Magnification
(magnitude)
1 larger
<1 smaller
Revised 5/30/1 8
