ESAT

wave speed

𝑐 = 𝑓λ

period

𝑓 = 1/T

photon energy

𝐸 = ℎ𝑓 = ℎ𝑐 / λ

law of refraction

𝑛1 sin 𝜃1 = 𝑛2 sin 𝜃2

critical angles

sin𝜃c = n2/n1 for n1>n2

refractive index

sin(i)/sin(r)

incoming angle

= reflective angle

snell's law

n2/n1 = v2/v1 = λ1/λ2 = 1/sin𝜃c

moments

Fd

velocity

𝑣 = ∆𝑠/∆t

acceleration

𝑎 = ∆𝑣/∆t

equations of motion

𝑣 = 𝑢 + 𝑎t

𝑠 = ((𝑢 + 𝑣)/2)t

𝑣² = 𝑢² + 2as

𝑠 = ut + (at²)/2

𝑠 = vt - (at²)/2

force

𝐹 = 𝑚a

𝐹 = ∆(𝑚v)/∆t

impulse

𝐹 Δ𝑡 = Δ(𝑚v)

work, energy

𝑊 = 𝐹 𝑠 cos 𝛳

energy (m)

𝐸m=𝐸c+𝐸p

energy (k)

𝐸k = 1/2 (𝑚𝑣²) = W

energy (p)

Δ𝐸p = 𝑚gΔℎ

power

∆𝑊/∆𝑡 = ∆E/∆𝑡 = Fv

gmh/t

Intensity

I=P/A

efficiency (𝜂)

useful output power

/ input power

Momentum conservation

m1v1+m2v2=m1v1'+m2v2'

density

𝜌 = 𝑚/V

Hooke’s law

𝐹 = 𝑘 Δe

Young Modulus

tensil stress / tensil strain

spring energy stored (EPE)

𝐸 = (1/2) 𝐹ΔL²

tensile stress

𝐹/A

tensile strain

∆𝐿 / 𝐿

Simple harmonic motion, spring

T = 2π√(m/k)

Simple harmonic motion, pendulum

T = 2π√(l/g)

elasticity modulus

T= λx/l

current

𝐼 = ∆𝑄/∆t

pd

V = RI (Ohms law)

V = W/Q

resistors in series

𝑅T = 𝑅1 + 𝑅2 + 𝑅3 + …

resistors in parallel

1/𝑅T =1/𝑅1 +1/𝑅2 +1/𝑅3⋯

springs in series

1/kT =1/k1 +1/k2 +1/k3⋯

springs in parallel

kT = k1 + k2 + k3 + …

power

𝑃 = 𝑉I = 𝐼²𝑅 = 𝑉²/R

emf

𝜀 = 𝐼(𝑅 + 𝑟) <=> E/Q

electrical capacity (Farad)

Q=CV => C=Q/V

resistivity

ρ = RA/L <=> R = ρL/A

Capacity energy stored

E=1/2 QV =1/2 CV² =1/2 Q²/C

gravitational field strength

𝑔 = 𝐹/m

force between 2 masses

𝐹 = (𝐺𝑚1𝑚2) /𝑟²

force " " 2 point charges

𝐹 = k(𝑄1𝑄2)/𝑟²

thermodynamics

Q=ΔU+W

W=pΔV

Q = m c ΔT

gas law

Pv = nRT = NkT

magnitude of angular speed

ω = v/r = dθ/dt = 2πf

centrepidal acceleration

a= v²/r = ω²r = ωv

centripedal force

F = mv²/r = mrω²

circular displacement

δ s = r δθ

Ideal velocity in a conical pendulum

v = √(gr tanθ)

alpha decay

-4m, -2a

beta decay

-0m, +1a

Pressure

P = F/A

P1V1 = P2V2

P= nRT/v (mol*constant*°K)

Tension

T=Fg​+Fnet​

Area of triangle =

1/2(a*b*sinC)

Circle equation =

(x - x_o)²+(y - y_o)² = r²

Binomial expansion ^3

(a+b)^3 = a^3 +3a²b +3ab²+ b^3

(a-b)^3 = a^3 -3a²b +3ab²- b^3

a^3-b^3 = (a-b)(a² + ab + b²)

Inverse pythagorus

a-² + b-² = h-² (no hypothenus)

tan0°

tan30°

tan45°

tan60°

0

1/√3

1

√3

logarithms (difference)

ln(a)−ln(b)=ln(a/b​)

aln(b)=ln(b^a)

perpendicular functions' product

m1*m2=-1

the sum of exterior angles =

360°

distance of two points

d=√(x2−x1)²+(y2-y1)²

cosine law

c² = a² + b² − 2ab cos(C)

S_infinity (geo)

a/(1-r)

S_n

a(1-r^n)/(1-r)

Newton's First Law (Law of Inertia)

A body at rest will remain at rest, and a body in motion will remain in motion at a constant velocity, unless acted upon by a net external force.

Explanation:

This law means that objects will not change their state of motion unless a force causes them to do so. In other words, if something is moving, it won't stop or change direction unless a force (like friction or a push) acts on it. Similarly, if it's at rest, it won't start moving unless a force is applied.

Newton's Second Law (Law of Acceleration)

The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The formula is F=ma.

Explanation:

This law quantifies how forces affect motion. It states that the greater the mass of an object, the more force is needed to accelerate it. Similarly, for a given mass, the acceleration increases as the applied force increases.

Newton's Third Law (Action and Reaction)

For every action, there is an equal and opposite reaction.

Explanation:

This law means that forces always come in pairs. When one object exerts a force on another, the second object exerts an equal and opposite force on the first. For example, when you push against a wall, the wall pushes back with equal force in the opposite direction.

Kepler's Second Law:

The imaginary line joining a planet and the Sun sweeps equal areas of space during equal time intervals as the planet orbits.

Kepler's Third Law:

Kepler's other (relevant) law: T^2 directly proportional to r^3 (where T is the time period for a planet orbiting a star, and r is the distance between the centres of the star and the planet in question

zeroth law of thermodynamics

If two bodies are each in thermal equilibrium with some third body, then they are also in equilibrium with each other.

first law of thermodynamics

energy can neither be created nor destroyed, only altered in form. For any system, energy transfer is associated with mass crossing the control boundary, external work, or heat transfer across the boundary.