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IOE Physics and Mathematics Formulas

Flashcards with the formulas most used in the IOE engineering entrance physics and mathematics sections. Original study material.

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Equation of motion without time

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Equation of motion without time

v^{2} = u^{2} + 2 a s

Range of a projectile at angle

θ

R = \frac{u ^{2} sin 2 θ}{g}

Maximum height of a projectile

H = \frac{u ^{2} sin ^{2} θ}{2 g}

Time period of a simple pendulum

T = 2 π L / g

Centripetal force

F = \frac{m v ^{2}}{r}

Coulomb's law

F = \frac{k q _{1} q _{2}}{r ^{2}}

, with

k = 9 \times 1 0^{9}

N m²/C²

Energy stored in a capacitor

U = \frac{1}{2} C V^{2}

Series capacitors

\frac{1}{C} = \frac{1}{C _{1}} + \frac{1}{C _{2}}

Photoelectric equation

K_{ma x} = h ν - ϕ

Lens formula

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

Carnot engine efficiency

η = 1 - \frac{T _{2}}{T _{1}}

with temperatures in kelvin

Radioactive decay after

n

half-lives

N = N_{0} / 2^{n}

Force on a current-carrying wire in a magnetic field

F = B I l sin θ

Beat frequency of two sounds

The difference of the two frequencies

Fundamental frequency of a stretched string

f = \frac{1}{2 L} T / μ

Derivative of

sin x

cos x

Derivative of

x^{n}

n x^{n - 1}

Integral of

x^{n}

for

n \neq = - 1

\frac{x ^{n + 1}}{n + 1} + C

Sum of an arithmetic progression

S_{n} = \frac{n}{2} [2 a + (n - 1) d]

Sum to infinity of a geometric series with

∣ r ∣ < 1

S = \frac{a}{1 - r}

Sum of the roots of

a x^{2} + b x + c = 0

- \frac{b}{a}

Product of the roots of

a x^{2} + b x + c = 0

\frac{c}{a}

Centre of the circle

x^{2} + y^{2} + 2 g x + 2 f y + c = 0

(- g, - f)

Determinant of a 2 x 2 matrix with rows

(a, b)

and

(c, d)

a d - b c

Modulus of

z = a + bi

a^{2} + b^{2}

det (k A)

for an

n \times n

matrix

k^{n} det A

Number of ways of choosing

r

items from

n

(r n) = \frac{n !}{r ! ( n - r )!}

Slope of a line perpendicular to a line of slope

m

- \frac{1}{m}

Heat needed to change temperature

Q = m c Δ T

Dimensional formula of work

[M L^{2} T^{- 2}]

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