Name Formula Variable definitions Uses/applications Comments

Pythagorean Theorem a2+b2=c2 a&b are legs of a right triangle and c is the hypotenuse

Find lengths of sides/magnitues of right triangle

Usually needs to be manipulated

Velocity average vav=∆x/∆t ∆x is total change in x, and ∆t is total change in t

Find velocity over a given distance and time

Very general usage

Specific distance equation

d=vavt d is distance Distance with given velocity and time

Several manipulations of this formula

Velocity Final vf=vi+at vf is final velocity, vi is initial velocity, a is acceleration, t is time

Gives final instantaneous velocity for given acceleration and time

Useful for most general kinematics problems

General distance equation

d=vit+at2/2All variables have been previousy noted

Gives final distance for a given initial velocity, acceleration, and time

The most useful general kinematics equation, you can cancel terms for many situations

Adjacent component Vad=Vcos θ V is hypotenuse, θ is angle between V and Vad, and Vad is adjacent component

Gives adjacent component of a triangle

Usually needed in a 2D problem

Opposite component Vopp=Vsin θ V is hypotenuse, θ is angle between V and Vopp, and

Vopp is adjacent component

Gives opposite component of a triangle

Usually needed in a 2D problem

Unknown angle tan-1 (Vopp/Vad)= θ tan-1 is also called arctan, it is the inverse tan of the ratio of Vopp over Vad

Finds the angle between two components

Useful when the problem asks for both magnitude and direction of vector

Centripetal acceleration

a=v2/ra is centripetal acceleration and is directed perpendicular to v, v is tangential velocity or instantaneous velocity, and r is the radius of the circle

Gives acceleration for a given velocity and radius

Centripetal force F=mv2/rF is force, m is mass Gives for for centripetal

accelerationNewton's 2nd Law F=ma F is force, m is mass, a is

accelerationMost useful equation for all force related problems

This equation has many manipulations and can be applied to many higher level problems

Gravitational Force F=Gm1m2/r2 G is the gravitational

constant, m1 and m2 are masses of the objects and r is the distance between the centers of masses of each object

General gravitation problems Don't forget that r2 is the distance between the center of masses of the objects

Orbital velocity v=√(Gme/r) me is mass of earth, or other planetary/large mass object

Orbital velocity Derived from taking Gravitational force = Fc the centripetal force

Kinetic Friction fk=µkN µk is the coefficient of kinetic friction

Friction of motion Opposes direction of motion

Static Friction fs≤µsN µs is the coefficient of static friction

Friction when there is no motion

Static friction acts for instances such as Centripetal force

Arc Length s=rθ s is the length of an arc ofa circle, r is radius and θ isthe angle traveled

Useful for finding totaldistance traveled inproblems where you have toconvert revolutions to an SIlike meters

Cartesian Conversion x=rcosθy=rsinθ

r is radius, and θ is angle

Angular Velocity ω=θ/t ω is angular velocity inradians per second, or nonSI is revolutions per second

There are many algebraicsubstitutions andmanipulations of and for ω

You might need the formulasheet to connect the dotson all conversions offormulas needed to solve acircular motion problem

PHYS 115 Formula Matrix

Angular Velocity in relation to Period

ω=2π/T 2π (π=pi) is not a variable,but a constant, T is period(seconds/cycle)

Can also be defined as 2πf,where f is frequency 1/T

Tangential Velocity vtan=rω vtan is velocity directedperpendicular to radius ofcircle

The x component of velocity,or what a speedometerwould read on a car goingaround a circle

Manipulation of Period T=2πr/v variables as above, v is vtan

Another definition of Angular velocity

ω=v/r v is vtan v/r is also s/(rt) Useful conversion

Work W=Fd W is work and has units of Joules, or Newton*meters

Simple formula for computing work. Work is always defined in the direction of motion, -W is against direction of motion

Power P=W/t P is power and has units of Watts, or Joules per second J/s

Work done over a specific time

Kinetic Energy KE=(1/2)mv2 KE is kinetic energy, has units of Joules

The velocity component can dnow be calculated from Kinetic Energy

Potential Energy PE=mgh PE is potential energy, has units of Joules, h depends on where you define your zero point

Energy of position, you must be consistent with defining your zero point

Conservation of Energy PEi + KEi = PEf + KEf PEi and KEi are initial

energies and PEf and KEf are final energies

Sum the initial energies and that will equal final energies

When more than one object is used the initial and final energies of each object must be calculated separately

Momentum p=mv p is momentum, no specific units are used, p is kg*m/s

General momentum equation

Impulse FΔt=Δp Δ is change, units are non specific as N*s which is as above kg*m/s

FΔt is force multiplied by the change in time, it will equal the change in momentum, or impulse

Impulse/Momentum FΔt=mΔv Variables as described above

A more useful manipulation of the above equation

Conservation of Momentum

Δpi=Δpf pi and pf are initial and final momentums

Sum of initial momentums will equal sum of final momentums

As in energy, if more than one object is present, the sum of the momentums of each object will have to be calculated separately

Spring Force F=-kx F is spring force, k is spring constant in N/m, and x is displacement of spring from equilibrium

A measure of the "restoring" force of the spring, can be used in work/energy relationships

Useful to find the spring constant, or force from spring constant, can be used with F=ma

Potential Energy of a Spring

U=(1/2)kx2 U is potential energy The potential energy in a spring that has been stretched or compressed a distance of x

Useful for problems where you have to find a velocity for a given (stretch/compress) on a spring due to the relationship of PE and KE

Frequency f=1/T f is frequency or cycles per second, T is period as seconds per cycle

frequency is defined by Hertz or Hz

Can simplify an equation

Angular velocity on a spring

ω=√(k/m) m is mass

Period, defined in multiple definitions

T=2π√(m/k) T=2π√(L/g)

L is length of string, or distance between center of mass and point of attachment, g is gravity

Period for a spring and a simple pendulum

SHM position x=Acosθ x=Acos(ωt) x=Acos((2π/T)t)

All are postion functions, t in equation 3 is time, for a given time the postion can be located

Where to find the object/particle along a path for a given angle, time, period, or angular velocity

SHM velocity v=-Aωsin(ωt) Velocity of particle/object in SHM can be found with equation given

SHM accleration a=-Aω2cos(ωt)Acceleratoin of particle/object in SHM can be found with given equation

SHM vmax vmax=Aω vmax is maximum velocity of particle/object in SHM

Maximum velocity is usually at equilibrium in SHM

SHM amax amax=Aω2 amax is maximum acceleration of particle/object in SHM