Science Formulae for Class 9

Science formula for class 9 is considered to be the foundation for the next three years. For the students who wish to proceed into the field of science, class 9 physics holds utmost importance because its syllabus is carried forward into the coming years. It is of utmost importance to have its basics cleared to build a robust base for further advancements and topics including electric current, optics, magnetism, laws of motion, etc. 

Keyterms: Electric current, Optics, Magnetism, Laws of motion, Length conversion, Time Unit conversion, Energy Unit conversion, Force Unit conversion, Viscosity Unit conversion

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Conversion of Units

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Length Conversion

1 mm  =  0.001 m

1 cm = 0.01 m

1 dm (1 decimeter) = 0.1 m

1 dcm (1 decameter) = 10 m

1 hm = 100 m

1 km = 1000 m

1 mile = 1.609 km

1 inch = 2.54 * 10?² m

1 foot = 3.05 * 10?² m

1 fermi = 10?¹? m

1 angstrom = 10?¹⁰ m

1 light year = 9.46 * 10¹⁵ m

Time Unit Conversion

1 min = 60 secs

1 hour = 3600 secs

1 day = 86400 secs

1 week = 604800 secs

1 year = 31536000 secs (365 days)

Energy Unit Conversion

1 erg = 10?? Joules

1 foot-pound = 1.356 Joules

1 kilowatt-hr = 3.6 * 10⁶ Joules

1 eV = 1.602 * 10¹⁹ Joules

1 calorie = 4.186 Joules

1 litre atmosphere = 101.13 Joules

Force Unit Conversion

1 dyne = 10^-5 Newton

1 pound = 4.448 Newton

Viscosity Unit Conversion

1 poise = 0.1 kg/m s

1 slug/ft = 47.9 kg/m s

Also Read: 

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Force and Laws of Motion

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Speed = total distance travelled / time taken [S = d/t]

Velocity = displacement / time [v = x/t]

acceleration = change in velocity / time [a = Δv/Δt]

acceleration = a = final velocity - initial velocity / time

[a = (v-u) / t]

The three equations of motion: 

(i) v = u + at  Relation between velocity and time

(ii) s = ut + 1/2at²  Relation between displacement and time

(iii) v² - u² = 2as  Relation between displacement and velocity

Rate of change of momentum = Δp/t

where, Δp = m(v-u)

In the absence of an external force, an object will remain in its state of motion/rest i.e., maintain inertia [First law of Motion]

The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object i.e., F = ma. [Second law of Motion]

For every action, there is an equal and opposite reaction [Third law of Motion]

Derivations of the three equations of motion:

v = u + at

Here, v is the final velocity, u is the initial velocity, a is acceleration and t is the time taken. 

Acceleration = change in the velocity / time taken

= (final velocity – initial velocity) / time taken

a = (v - u) / t

at = v – u

v = u + at

s = ut + ½ at²

We know that displacement = average velocity * time

Displacement = {(initial velocity + final velocity) / 2 } * time

s = {(u + v) / 2} * t

From the first equation of motion, we know that v = u + at

Substituting this value of v into this equation, we get

s = [ {u + (u + at)} / 2 ] * t

s = {(2u + at) / 2 } * t

s = {(2u / 2) + (at / 2)} * t

s = (u + ½ at) * t

s = at + ½ at²

v² – u² = 2as

From the first equation of motion, we know that v = u + at

v-u = at

t = (v - u) / a

displacement = average velocity * time

s = {(u + v) / 2} * t

s = {(v  + u) / 2 } * {(v  - u) / a }

s = (v² – u²) / 2a

2as = v² – u²

v² – u² = 2as

Derivation of the Second Law of Motion:

The statement of this law states that:

F ∝ change in momentum / time taken

We know that change in momentum = mv – mu

Hence, the law becomes

F ∝ (mv – mu) / t

F ∝ m (v – u) / t

But (v -u) / t = acceleration

Hence,

F ∝ ma

F = kma [k is the constant of proportionality whose value is taken to be 1]

F = ma

This is the second law of motion.

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Gravitation

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The force exerted by an object on another object is proportional to the product of their masses and is inversely proportional to the square of the distance between them.

F = G (M¹*M²/d²)

Where G = 6.673 * 10^-11 is Universal Gravitation Constant [Nm²Kg?²]

Derivation: 

From the statement, we can write that

F ∝ (M¹ * M²) / d²

F = G (M¹*M²/d²)  [Here, G is the constant of proportionality whose value is 6.673 * 10^-11 Nm²kg?²]

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Work and Energy 

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The work done is defined as the product of the force in the direction of the displacement and the magnitude of the object’s displacement.

W = (F cosθ) *s Joules 

When angle is 0, 

W = F * s

Energy is the ability of an object to do work. It has two primary forms – Kinetic and Potential. Energy stored is referred to as Potential Energy while that which we observe while in motion is called Kinetic energy.

K.E. = ½*( mv² )

P.E. = mgh 

Also Read: 

Work – Energy Theorem

This theorem states that the total work done by all the forces combined is equal to the change in kinetic energy of the object. 

W = ΔK = K Final  - K Initial

Derivation of Kinetic Energy Formula:

We know that W = F Δs = ma Δs

Now, from the third equation of motion,

v² = u² + 2aΔs

aΔs = (v² – u²) / 2

Combining these, we get

ΔK = m * ((v² – u²) / 2)

ΔK = ½ mv² – ½ mu²

We know that the kinetic energy of a body at rest is zero.

Hence, 

K = ½ mv²

Derivation of Potential Energy Formula

We know that W = Force * Displacement

Therefore, for a body of mass m that is being raised to a height h with g being the gravitational force acting on it,

W = mg * h

W = mgh

When the body is at rest, its Kinetic Energy is zero.

Hence, according to the work energy theorem, 

Potential Energy = mgh

P.E. = mgh

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Sound

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A form of mechanical energy that is created by the vibration of objects via propagation through a medium

The number of oscillations performed per second are measured using frequency ν (Hz)

The time taken per oscillation is called Time Period (T)

The distance between two consecutive crests or falls is called the Wavelength (λ)

A few noteworthy relations are:

ν = 1 / T

Sound of Speed Wave v = ν λ 

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Things to Remember

• v = u + at
• s = at + ½ at²
• v² – u² = 2as
• F = ma
• The kinetic energy of a body at rest is zero.
• All objects have a tendency to maintain inertia.
• Gravitational force is the force between two bodies while the force of gravity is the force between the earth’s surface and any object.
• Sound comes from vibrations which create sound waves.
• Sound requires a medium to travel. Hence, it cannot propagate through vacuum. 

Also Read: 

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