All equations needed Flashcards by TOMMY DICAPRI

General velocityequation

v = Δs/Δt = m/s =ms^-1

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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

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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)

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Derive v=u+at

acceleration = v-u/t
rearrange for v
v=u+at

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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

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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

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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

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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

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Projectile motion Horizontal component
(THIS LINK HAS THE TRIANGLE NEEDED)(https://discover.hubpages.com/education/AS-Level-Physics-Formula-Sheet)

x = v cos 0

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Equation for newtons second law

F = ma

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Weight of an object equation

W = mg

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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

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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

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What is moment of force

Moment of force is the product of that force and the perpendicular distance between that force and the pivot

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Moment of force equation

moment = F x X = N x m = Nm

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moment equation when force is perpindicular?

F x d

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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

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Rate of change of momentum is _________ to the resultant force acting on it

Directly proportional

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linear momentum equation

p = mv

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Conservation of momentum

Momentum before a collision is equal to the momentum after a collision,as long as there is no external resultant force.

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The sum of moments about a pivot

The sum of moments about a pivot is always zero

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What is a couple

A sytem of forces with a resultant moment of force but no resultant force

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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

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Work done equation

W = F x s
f(force)
s(displacement)
orW = fxcos0
x(displacement)

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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