Download Formula Matrix 3

PHYS 115 Formula Matrix
Name
Formula
Pythagorean Theorem
a2+b2=c2
Velocity average
vav=∆x/∆t
Specific distance
equation
Velocity Final
d=vavt
General distance
equation
d=vit+at2/2
Adjacent component
Vad=Vcos θ
Opposite component
Vopp=Vsin θ
vf=vi+at
Variable
definitions
a&b are legs of a right
triangle and c is the
hypotenuse
∆x is total change in x, and
∆t is total change in t
d is distance
vf is final velocity, vi is
initial velocity, a is
acceleration, t is time
All variables have been
previousy noted
V is hypotenuse, θ is angle
between V and Vad, and Vad
is adjacent component
V is hypotenuse, θ is angle
between V and Vopp, and
Vopp is adjacent component
Unknown angle
tan-1 (Vopp/Vad)= θ
Centripetal
acceleration
a=v2/r
Centripetal force
F=mv2/r
F is force, m is mass
Newton's 2nd Law
F=ma
F is force, m is mass, a is
acceleration
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
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
Orbital velocity
v=√(Gme/r)
me is mass of earth, or other
planetary/large mass object
Kinetic Friction
fk=µkN
Static Friction
fs≤µsN
Work
W=Fd
W is work and has units of
Joules, or Newton*meters
Power
P=W/t
Kinetic Energy
KE=(1/2)mv2
P is power and has units of
Watts, or Joules per second
J/s
KE is kinetic energy, has
units of Joules
Potential Energy
PE=mgh
Conservation of Energy PEi + KEi = PEf + KEf
µk is the coefficient of
kinetic friction
µs is the coefficient of static
friction
PE is potential energy, has
units of Joules, h depends
on where you define your
zero point
PEi and KEi are initial
energies and PEf and KEf
are final energies
Momentum
p=mv
p is momentum, no specific
units are used, p is kg*m/s
Impulse
FΔt=Δp
Δ is change, units are non
specific as N*s which is as
above kg*m/s
Impulse/Momentum
FΔt=mΔv
Conservation of
Momentum
Δpi=Δpf
Variables as described
above
pi and pf are initial and final
momentums
mula Matrix
Uses/applications
Comments
Find lengths of
Usually needs to be
sides/magnitues of right
manipulated
triangle
Find velocity over a given
Very general usage
distance and time
Distance with given velocity Several manipulations of
and time
this formula
Gives final instantaneous
velocity for given
acceleration and time
Gives final distance for a
given initial velocity,
acceleration, and time
Useful for most general
kinematics problems
The most useful general
kinematics equation, you
can cancel terms for many
situations
Gives adjacent component of Usually needed in a 2D
a triangle
problem
Gives opposite component of Usually needed in a 2D
a triangle
problem
Finds the angle between two Useful when the problem
components
asks for both magnitude
and direction of vector
Gives acceleration for a
given velocity and radius
Gives for for centripetal
acceleration
Most useful equation for all
force related problems
This equation has many
manipulations and can be
applied to many higher
level problems
General gravitation problems Don't forget that r2 is the
distance between the
center of masses of the
objects
Orbital velocity
Friction of motion
Friction when there is no
motion
Derived from taking
Gravitational force = Fc the
centripetal force
Opposes direction of
motion
Static friction acts for
instances such as
Centripetal force
Simple formula for
computing work. Work is
always defined in the
direction of motion, -W is
against direction of motion
Work done over a specific
time
The velocity component can
dnow be calculated from
Kinetic Energy
Energy of position, you must
be consistent with defining
your zero point
Sum the initial energies and When more than one object
that will equal final energies is used the initial and final
energies of each object
must be calculated
separately
General momentum
equation
FΔt is force multiplied by the
change in time, it will equal
the change in momentum,
or impulse
A more useful manipulation
of the above equation
Sum of initial momentums
As in energy, if more than
will equal sum of final
one object is present, the
momentums
sum of the momentums of
each object will have to be
calculated separately