All equations needed Flashcards
General velocityequation
v = Δs/Δt = m/s =ms^-1
Acceleration equation
a =Δv/Δt = ms^-1/s = ms^-2
(Keep in mind if you are not finding acceleration by that I mean if the question does not ask you specifically then acceleration is always 9.8 as 9.8 is the acceleration of gravity
Acceleration equation of motion derived from one of the suvats?
rearranging v=u+at for a a = v - u/t
(v = final velocity, u = initial velocity)
(Note: that most times when finding verticals and horizontal components the vertical component is almost always a suvat equation)
Derive v=u+at
acceleration = v-u/t
rearrange for v
v=u+at
Derive s=(u+v)/2 t
average velocity = v+u/2
displacement = s=s+vt
sub v(average) in s
s=s+(v+u)/2
inital displacement 0
s=(u+v)/2 t
Derive s = ut+1/2 at^2
Sub v=u+at into s = 1/2(u+v)
s= 1/2(u+(u+at))t
simplify:
s=1/2(2u +uat)t =
s=1/2 ut +at^2
s=ut+ 1/2at^2
Derive v^2 = u^2 + 2as
Square v=u=at
v^2=u^2+2uat +at^2
rearrange s = ut + 1/2 at^2 for at^2
at^2 = 1/2 s-ut
remove the 1/2
at^2 = 2s - 2ut
sub into v^2
v^2 = u^2 + 2uat + a(2s - 2ut)
simplify:
v^2 = u^2 +2uat + 2as - 2uat
v^2 = u^2 + 2as
Projectile motion vertical component
(THIS LINK HAS THE TRIANGLE NEEDED)(https://discover.hubpages.com/education/AS-Level-Physics-Formula-Sheet)
(v = initial velocity)
y = v sin 0
Projectile motion Horizontal component
(THIS LINK HAS THE TRIANGLE NEEDED)(https://discover.hubpages.com/education/AS-Level-Physics-Formula-Sheet)
x = v cos 0
Equation for newtons second law
F = ma
Weight of an object equation
W = mg
Resolving Components of a force, Horizontal component (CHECK THIS LINK FOR DIAGRAM)(https://discover.hubpages.com/education/AS-Level-Physics-Formula-Sheet)
Gives the direction of downward force which is causing acceleration
F = mg sin 0
a = f/m = mg sin 0/m = g sin0
Resolving Components of a force, Vertical component (CHECK THIS LINK FOR DIAGRAM)(https://discover.hubpages.com/education/AS-Level-Physics-Formula-Sheet)
Gives the amount of force exerted by the object on inclined plane or vice versa
F =mg cos 0
What is moment of force
Moment of force is the product of that force and the perpendicular distance between that force and the pivot
Moment of force equation
moment = F x X = N x m = Nm
moment equation when force is perpindicular?
F x d
Moment when force is not perpendicular(Check example on LINK)(https://discover.hubpages.com/education/AS-Level-Physics-Formula-Sheet)
You will need to break the force into components to find which component is perpendicular to the line of action.
moment = F sin 0 x d
Or find the perpindicular distance between that force and pivot as another way around.
moment = d sin 0 x F
Rate of change of momentum is _________ to the resultant force acting on it
Directly proportional
linear momentum equation
p = mv
Conservation of momentum
Momentum before a collision is equal to the momentum after a collision,as long as there is no external resultant force.
The sum of moments about a pivot
The sum of moments about a pivot is always zero
What is a couple
A sytem of forces with a resultant moment of force but no resultant force
Torque of Couple(check diagram seriously ON LINK)(https://discover.hubpages.com/education/AS-Level-Physics-Formula-Sheet)
F1 = F2
F1 or F2 x (d1 + d2) = torque
Work done equation
W = F x s
f(force)
s(displacement)
orW = fxcos0
x(displacement)
Work done Joules equation
joules = N x m = nm = (f x d) (n = newtowns, m = metres)
Gravitational potential energy equation
Eg = mgh
Kinetic potential energy
Ek = 1/2mv^2
Gravitational Potential energy- Kinetic energy(G.P.E, K.E) transformations, Going down
Going down, P.E changes into K.E, height decreases, v increases
G.P.E-K.E transformations Going up
K.E changes into P.E, height increases, v decreases
Power equation
p = W/t = j/t = watts
Power developed by a moving object equation
P = F x v
Work done by an expanding gas
Force is equal to pressure x area.
F = p x A
Word done equal to force x distance moved
W = p x A x s
Area x length moved is change in volume
W = pΔv
Equation defining momentum
p = m x v = kgms^-1
Impulse equation
F = Δp/Δt = m(v-u)/t
Newtons first law stated in terms of momentum
An object moving with constant velocity has constant momentum because its mass and velocity is constant.
Newtons second law stated in terms of momentum
Net force acting on an object is proportional to the rate of change of momentum. Both have same directions
Newtons third law stated in terms of momentum
Total momentum in a system remains constant and conserved.
Displacement equation
x = v x t
Total momentum before and after the collision must remain what?
constant
Hooks law
Extension x in a spring is directly proportional to the force F applied on it.
x directly proportional F
Or adding a proportionality constant called the ‘force constant’
F = Kx
Equation for stress
stress = force/cross sectional Area
what are the units of Stress
N/m^2
Equation for strain
strain = extension/original length (X/L)
What are the units of strain
There are no units of strain as it is a ratio
Young modulus equation
Young modulus = stress/strain
Energy stored inside a spring
Energy stored inside a spring is equal to the area under force extension graph.
Or 1/2 x F x X
Or = 1/2 x KX x X = kX^2
Elastic field strength, when force and charge are given
E = F/Q (NC^-1)
Elastic field strength, when potential difference and distance is given
E = - v/d (vm^-1)
Electric potential
V = W/Q
Force on a charge in electric field
F = - QV/d
if the charge is an electron Q = -e
Equation for the effect of gravity on a charge travelling in a electric field
F = m
Current equation
Current = charge/time = Δq/Δt
Voltage equation
v = work done by charge or energy dissipated/unit charge
v = W/Q
Resistance equation
Resistance of an electrical component is defined as the ration of voltage and current across it.
R = V/I
What is resistance measured in
Resistance is measured in ohms.
Original expression of power
p = W/t
Electrical power equations
can be derived from the original expression of power.
Work done by a charge when it moves across a potential difference is given by W = V x Q
If you replace I by V/R it becomes:
P = V^2/R
If you replace V by I x R it becomes: P = I^2R
Electrical energy equation
P = E/t
E = P x t
E = V x l x t
Resistivity equation
R = pl/A
Where:
R = resistance
A = cross sectional area of conductor
l = length of conductor
p = resistivity constant(different for every material)
Kirchhoff’s current law
The sum of currents at a junction is always zero.
Currents entering a junction will be + positive, currents leaving will be - negative
Kirchhoff’s voltage law
The sum of voltage drops or potential differences around a closed loop is equal to the sum of e.m.fs or voltage sources
Internal resistance of a battery
Represented by adding a resistor in series with a battery e.g apply Kirchhoff’s battery e.m.f = lR1 + lR2
E = lR1 + lR2
The terminal potential difference(v)across the battery terminals will now be: E - lR1 = V
Potential Divider
Divides the voltage between two points. (The numerator is always the resistor which the voltage has to be determined). (Denominator is the sum of resistances) e.g
V2 = R2/ R1 + R1 x V1
Resistors in series
Rr = R1 + R2 + Rn
Resistors in parallel
1/RT = 1/R1 + 1/R2 + 1/Rn
Resistors of same value in parallel
If two resistors of the same value are connected in parallel then the equivalent (total) resistance will be equal to half the resistance of one of the resistors.
e.g. Two resistors of 40 ohms total resistance would be 20 ohms.
Frequency of a wave equation
f = 1/T
number of oscillations per second, measured in hertz
intensity
Rate of energy transmitted per unit area at right angles to the wave velocity .
Intensity equation
intensity = power/cross sectional area
measured in(Wm-2).
The wave equation
velocity = frequency x wave length
v = f x wave length symbol
radio waves, wavelength range
10^6 to 10^-1
microwaves, wavelength range
10^-1 to 10^-3
infrared, wavelength range
10^-3 to 7 x 10^-7
visible, wavelength range
7 x 10^-7 to 4x10^-7
ultraviolet, wavelength range
4 x 10^-7 to 10^-8
x-rays, wavelength range
10^8 to 10^-13
y- rays wavelength range
10^-10 to 10^-16
Neutrons equation
Neutrons =Ar - number of protons
Mole equation
mole = mass of substance/Mr/Ar
Number of particles in 1 mole of substance
Number = Av x no.of moles
Density of substance equation
density = mass/volume = kg/m^3 = kgm^-3
Volume of an atom
Vol. = total volume of substance/number of particles in substance
Number remaining after ‘n’ half lives
number =(1/2)^n x total number of particles
