Physics And Maths Formulae Flashcards
Equation relating change in displacement with acceleration, time and original velocity?
Δx = 1/2 at^2 + Vot
Equation relating final velocity, original velocity, acceleration and time?
Vf =Vo +at
Equation relating total displacement with acceleration, time, original velocity and original displacement?
xf =1/2 at^2 + Vot + xo
Equation relating final velocity with acceleration, distance and original velocity?
Vf^2 = Vo^2 + 2ad
Equation relating displacement with time, original and final velocities?
x = (Vo+Vf)/2 x t
Sin0°?
Sin0° = 0
Sin60°?
Sin60° = √3/2
Cos0°?
Cos0° = 1
Cos60°?
Cos60° = ½
Tan0°?
Tan0° = 0
Tan60°?
Tan60° = √3
Equation for centripetal force?
ac = v^2/r
Force of gravity / Newton’s equation?
Fg = Kg m1m2/r^2
Given projectile velocity and angle, what is the equation for the original vertical component of velocity?
Voy = Vo sinθ
Vertical displacement given vertical velocity, time and acceleration of gravity?
y = Voyt + 1/2gt^2
Vertical component of velocity, given original vertical velocity, acceleration of gravity and time elapsed?
Vy =Voy +gt
Given projectile angle and magnitude, what is the horizontal component velocity?
Vox = VoCosθ
Given horizontal velocity and time, what is the horizontal component of displacement?
X = Voxt
Given the original horizontal velocity, what is the horizontal velocity?
Vx = Vox
Given the horizontal and vertical components of velocity in a projectile motion problem, what is the formula for the resolved projectile velocity?
Vo = √(Vox^2 + Voy^2)
Given x and y components of velocity, what formula gives the angle of projectile?
Tanθ = Vox/Voy
Formula for tension in a string?
T = 2 x g x m1m2 / m1+m2
Maximum friction formula?
f = μN
Acceleration in a pulley system problem?
a=F/m
Conservation of momentum in elastic collision?
m1v1 + m2v2 = m1v’ + m2v’’
Conservation of momentum in an inelastic collision?
m1v1 +m2v2 =v’(m1 +m2 )
Formula for momentum?
p = mv
Formula for impulse?
J = Δmv
Formula for kinetic energy?
Ek = 1/2mv^2
Formula for gravitational potential energy?
PE = mgh
Formula for torque force?
L=Fxr
Rotational equilibrium?
ΣCW = ΣCCW
Formula for work?
W=Fxd
How do you calculate the work done on an object by a force which isn’t in the precise direction of the movement?
W = F x d x Cosθ
What is the work energy theorem, what does it mean and when is it used?
W=ΔEk + ΔEp
It means that the work done by a resultant force on a particle is equal to the change in kinetic energy of that particle. It is used when work is done on a system therefore conservation of energy doesn’t apply.
How is the force in a spring calculated?
Fs = -Kx
Total mechanical energy in a system?
Etotal = Ek + Ep
Given the spring constant and displacement, how is the total work done on a spring calculated?
W = ½ Kx^2
What is the formula for Power?
P = ΔW/Δt (rate of doing work)
Given the density of a substance, how is specific gravity calculated?
SG = ρs/ρw
What is pressure?
P=F/A
How does pressure vary with depth?
ΔP = ρgΔh
What is the continuity equation? What is it used for?
ρvA = constant, ρv1A1 + ρv2A2
It shows that the flow is constant throughout a pipe
What is Bernoulli’s principle? What is it’s formula?
P + 1/2ρv2 + ρgh = constant
An increase in the speed of a fluid occurs simultaneously with a decrease in pressure or potential energy
What is flow?
R = Avt/t = Av
Flow is the volume past a point per unit of time
What is Archimedes principle?
Fg =vρg=mg
The force with which a floating object is buoyed up is equal to the weight of the water that it displaces.
What is Pascal’s law?
An external pressure applied to an enclosed fluid is transmitted uniform throughout
What is stress?
σ=F/A
What is strain?
ε, Relative change in dimensions caused by stress
What is the modulus of elasticity?
ME = σ / ε
What is frequency?
f = 1 second / T
Measured in hertz
What equation relates velocity of a wave, wavelength and the frequency?
v = λf
What equation gives the energy for a wave?
E = hf
What is formula gives the change in decibels?
ΔdB = 10log I/Io
What formula gives the period for a pendulum?
T = 2π √l/g
What frequency does a pipe/string closed at both ends or open at both ends oscillate at?
fn =nv/2L
n takes all integers
A string/pipe closed at one end oscillates with what frequency?
fn =nv/4L
n takes odd integers only
What is the equation for the period of a spring?
T = 2π √m/k
What equation gives intensity of sound?


I=P/A
What is the equation for calculating the Doppler effect? When do you use plus or minus?
fo = fs (v±vo) / (v±vs)
In deciding which sign to use, remember that frequency increases moving towards each other. Frequency observed will be higher when the first brackets are relatively higher than the second and vice versa.
Which formula shows the charge of a single proton or electron?
q = ne
What is Coulomb’s law?
F = (kq1q2)/r^2
What formula gives the strength of an electric field?
E = F/q = kq/d2
What is the formula for voltage?
V = Ep/q = kQ/r
What equation gives the relationship between voltage, current and resistance?
V = IR, I = V/R, R = V/I Ohm’s law
Given qualities of the medium, what equation gives the resistance?
R = ρl/A
How do you calculate resistance in series?
Rtotal = R1 + R2
How do you calculate resistance in parallel?
1/Rtotal = 1/R1 + 1/R2
How do you calculate capacitors in series?
1/Ceq = 1/C1 + 1/C2
How do you calculate capacitors in parallel?
Ceq =C1 +C2
What is Kirchoff’s 1st law?
Σi = 0
*In a junction the sum of currents approaching and leaving junction equals zero
What is Kirchoff’s 2nd law?
i1R1 +i2R2 -ε=0
Sum of voltage changes in a loop equal to zero
What is the root-mean-square formula for current?
Irms = Imax/√2
What equation relates object distance, image distance and focal length?
1/f = 1/i + 1/o
What is the formula for index of refraction?
n=c/v
Where c is the speed of light in a vacuum and v is the speed of light through the medium
What formula allows you to use the half life to calculate how much of something is left?
Nnt = No(½)^n
What formula gives the quantity of something after a certain number of doubling periods?
Nnt = 2n
What formula relates the energy with mass involved in nuclear binding?
E = mc2
What formula gives the number of electrons in a shell, n?
e = 2n^2
Sin30°?
Sin30° = ½
Sin45°?
Sin45° = 1/√2
Sin90°?
Sin90° = 1
Sin180°?
Sin180° = 0
Cos30°?
Cos30° = √3/2
Cos45°?
Cos45° = 1/√2
Cos90°?
Cos90° = 0
Cos180°?
Cos180° = -1
Tan45°?
Tan45° = 1
Tan30°?
Tan30° = 1/√3
Tan90°?
Tan90° = ∞
Tan180°?
Tan180° = 0
In a 30-60-90 triangle, what is the ratio of side lengths?
1, √2, 3, respectively
In a 45-45-90 triangle, what is the ratio of side lengths?
1, 1, √2, respectively
Approximately, what is the square root of 3?
1.7
Approximately, what is the square root of 2?
1.4
Approximately, what is pi?
3.14
How is slope calculated?
“Rise over run”.
Note that if it’s sloping downwards, the “rise” would be negative and therefore the slope would be as well
a^0 = ?
1
a^1 = ?
a
a^n a^m = ?
a^(n+m)
(a^n)^m = ?
a^(n+m)
a^(1/n) = ?
n√a
In practise logarithmic scales are used to do what?
Convert a rapidly changing curve into a straight line
Log (sub a) a = ?
1
Log (sub a) M^k = ?
k log (sub a) M
Log (sub a) MN = ?
Log (sub a) M + log (sub a) N
Log (sub a) M/N = ?
Log (sub a) M - log (sub a) N
a^-m = ?
1/ a^m
