The torque of a force has a magnitude that is given by the magnitude F of the force times the lever arm : = F . The lever arm is the perpendicular distance between the line of action of the force and the axis of rotation. A rigid body is in equilibr
A wave is a traveling disturbance and carries energy from place to place. In a transverse wave, the disturbance is perpendicular to the direction of travel of the wave. In a longitudinal wave, the disturbance is parallel to the line along which the w
Convection is the process in which heat is carried by the bulk movement of a fluid. During natural convection, the warmer, less dense part of a fluid is pushed upward by the buoyant force provided by the surrounding cooler and denser part. Forced con
Thermodynamics is the branch of physics built upon the laws obeyed by energy in the form of work and heat. A thermodynamic system is the collection of objects on which attention is being focused, and the surroundings are everything else. The state of
Fluids are materials that can flow. The mass density of any substance is its mass m divided by its volume V: = m/V. In the presence of gravity, the upper layers of a fluid push downward on the layers beneath, with the result that fluid pressure is
Displacement is a vector that points from an object's initial position toward its final position. The magnitude of the displacement is the shortest distance between the two positions. The average speed of an object is the distance traveled by the obj
Chapter 13 - "The Transfer of Heat"
Convection the process in which heat is carried from place to place by the bulk movement of a fluid. Conduction the process whereby heat is transferred directly through a material, with any bulk motion of the mat
In uniform circular motion, an object of mass m travels at a constant speed v on a circular path of radius r. The period T of the motion is the time required for one revolution. The speed, the period, and the radius are related according to v = 2r/T.
Chapter 10-15 Formulas
Chapter 10 - "Elasticity and Simple Harmonic Motion" Hooke's Law
F s kx
F s spring force , k spring constant , x displacement
k x m
a acceleration , m mass
Simple Harmonic Motion
2 1 2 f f
Chapter 7 - "Impulse and Momentum"
p mv Impulse Ft p linear momentum
Ft mv f mv o
Principle of Conservation of Linear Momentum The total linear momentum of an isolated system remains constant (is conserved).
Chapter 3 - "Kinematics in Two Dimensions"
y v o
v x v x v o cos o constant o x = v x t (v o cos o )t o vy vy y vy t
gt v o sin o gt
1 2 1 gt (v o sin o )t gt 2 2 2
2 2 v y v y 2gy (v o s
Chapter 6 - "Work and Energy"
W (F cos )s 1 joule = 1 newton - meter
1 mv 2 2
KE Kinetic Energy
W KEf KE o
1 1 2 mv f 2 mv o 2 2
PE mgh PE Gravitational Potential Energy
W gravity mgho mghf
Chapter 9 - "Rotational Dynamics"
torque = F
F force lever arm
Equilibrium of a Rigid Body
Center of Gravity
W 1 X 1 W 2 X 2 W 1 W 2
(moment of inertia )
Chapters 16 and 17 Formulas
Chapter 16 - "Waves and Sound"
f frequency , T period
v f v velocity , wavelength , f frequency
Speed of Wave in Stretched String
F tension force , m L m
Physics is an experimental science that uses precisely defined units of measurement. This text emphasizes SI (Systeme International) units, a system that includes the meter (m), the kilogram (kg), and the second (s) as base units for length, mass, an
There must be at least one source or generator of electrical energy in an electric circuit. The electromotive force (emf) of a generator, such as a battery, is the maximum potential difference (in volts) that exists between the terminals of the gener
Chapter 2 - "Kinematics in One Dimension"
x x x o v t t to
v = average velocity x = displacement t = time
x t 0 t
v = instantaneous velocity
v v v o t t to
a = average acceleration
v t 0 t
a = instantaneous acceleratio
Chapter 12 - "Temperature and Heat" T = Tc + 273.15
T = Temperature in Kelvins, Tc = Temperature in Celsius degrees Linear Thermal Expansion
L = L0T
L0 = original length, = coefficient of linear expansion, L = change in length, T = change in tempe
When a rigid body rotates about a fixed axis, the angular displacement is the angle swept out by a line passing through any point on the body and intersecting the axis of rotation perpendicularly. The radian (rad) is the SI unit of angular displaceme
Each element in the periodic table is assigned an atomic mass. One atomic mass unit (u) is exactly one-twelfth the mass of an atom of carbon-12. The molecular mass of a molecule is the sum of the atomic masses of its atoms. The number of moles n cont
When work WAB is done by an electric force as a posi-tive test charge +q0 moves from point A to point B, the work equals the electric potential energy EPE at A minus that at B: WAB = EPEA - EPEB. The electric potential V is the electric potential ene
Motion in two dimensions can be described in terms of the time t and the x and y components of four vectors: the displacement, the acceleration, the final velocity, and the initial velocity. The motion can be analyzed by treating the x and y componen
Chapter 20 - "Electric Circuits"
I = current (amperes) q = charge (coulombs) t = time (seconds)
Resistance and Resistivity
V = voltage (volts) I = current (amperes) R = resistance (ohms)
= resistivity (ohm-m) L = l
Chapters 1-9 Formulas Chapter 1 - "Introduction and Mathematical Concepts"
Trigonometry Review - Vector
c a b
a2 b2 c2
A A x
A x A cos
Ay = A sin
Chapter 19 - "Electric Potential Energy and the Electric Potential"
1 electron volt = 1.6 x 10-19 J
V = Electric potential (J/C = V) EPE = Electric Potential Energy (J) qo = test charge (C)
E = electric field (
Newton's first law of motion or law of inertia states that an object continues in a state of rest or in a state of motion at a constant speed along a straight line unless compelled to change that state by a net force. Inertia is the natural tendency
On the Celsius temperature scale, there are 100 equal divisions between the ice point (0 C) and the steam point (100 C). On the Fahrenheit temperature scale, there are 180 equal divisions between the ice point (32 F) and the steam point (212 F). For
The principle of linear superposition states that when two or more waves are present simultaneously at the same place, the resultant disturbance is the sum of the disturbances from the individual waves. Constructive interference occurs at a point whe
The force that must be applied to stretch or compress an ideal spring is FApplied = kx, where k is the spring constant and x is the displacement of the spring from its unstrained length. A spring exerts a restoring force on an object attached to the