Download Formula Matrix 2

PHYS 115 Formula Matrix
Name
Pythagorean Theorem
Formula
2
2
2
a +b =c
Velocity average
vav=∆x/∆t
Specific distance
equation
Velocity Final
d=vavt
vf=vi+at
General distance
equation
d=vit+at /2
Adjacent component
Vad=Vcos θ
Opposite component
Vopp=Vsin θ
2
Variable
definitions
Uses/applications
Comments
a&b are legs of a right
Find lengths of
Usually needs to be
triangle and c is the
sides/magnitues of right
manipulated
hypotenuse
triangle
∆x is total change in x, and Find velocity over a given
Very general usage
∆t is total change in t
distance and time
d is distance
Distance with given velocity Several manipulations of
and time
this formula
vf is final velocity, vi is
initial velocity, a is
acceleration, t is time
All variables have been
previousy noted
Gives final instantaneous
velocity for given
acceleration and time
Useful for most general
kinematics problems
Gives final distance for a
given initial velocity,
acceleration, and time
The most useful general
kinematics equation, you
can cancel terms for many
situations
V is hypotenuse, θ is angle Gives adjacent component of Usually needed in a 2D
problem
between V and Vad, and Vad a triangle
is adjacent component
V is hypotenuse, θ is angle Gives opposite component of Usually needed in a 2D
a triangle
problem
between V and Vopp, and
Vopp is adjacent component
tan-1 is also called arctan, it
is the inverse tan of the
ratio of Vopp over Vad
a is centripetal acceleration
and is directed
perpendicular to v, v is
tangential velocity or
instantaneous velocity, and
r is the radius of the circle
Finds the angle between two Useful when the problem
components
asks for both magnitude
and direction of vector
F=mv2/r
F is force, m is mass
Newton's 2nd Law
F=ma
F is force, m is mass, a is
acceleration
Gives for for centripetal
acceleration
Most useful equation for all
force related problems
Gravitational Force
F=Gm1m2/r2
Orbital velocity
v=√(Gme/r)
Kinetic Friction
fk=µkN
Static Friction
fs≤µsN
Arc Length
s=rθ
Cartesian conversion
x=rcosθ
y=rsinθ
ω=θ/t
G is the gravitational
General gravitation problems Don't forget that r2 is the
constant, m1 and m2 are
distance between the
masses of the objects and r
center of masses of the
is the distance between the
objects
centers of masses of each
object
Derived from taking
me is mass of earth, or other Orbital velocity
Gravitational force = Fc the
planetary/large mass object
centripetal force
Friction of motion
Opposes direction of
µk is the coefficient of
motion
kinetic friction
Static friction acts for
µs is the coefficient of static Friction when there is no
motion
instances such as
friction
Centripetal force
s is the length of an arc of Useful for finding total
a circle, r is radius and θ is distance traveled in
the angle traveled
problems where you have to
convert revolutions to an SI
like meters
r is radius, and θ is angle
Unknown angle
tan-1 (Vopp/Vad)= θ
Centripetal
acceleration
a=v2/r
Centripetal force
Angular velocity
Angular velocity in
relation to period
ω=2π/T
Tangential velocity
vtan=rω
Gives acceleration for a
given velocity and radius
ω is angular velocity in
There are many algebraic
radians per second, or non substitutions and
SI is revolutions per second manipulations of and for ω
2π (π=pi) is not a variable,
but a constant, T is period
(seconds/cycle)
vtan is velocity directed
perpendicular to radius of
circle
Can also be defined as 2πf,
where f is frequency 1/T
The x component of velocity,
or what a speedometer
would read on a car going
around a circle
This equation has many
manipulations and can be
applied to many higher
level problems
You might need the formula
sheet to connect the dots
on all conversions of
formulas needed to solve a
circular motion problem
Manipulation of Period T=2πr/v
variables as above, v is vtan
Another definition of
angular velocity
v is vtan
ω=v/r
v/r is also s/(rt)
Useful conversion