Impulse Units: Formula, SI Units & Example

Impulse units are used to measure the impulse of a force. Impulsive force is the force applied for a short period of time. For example, kicking a ball. The impulse of a force is the measure of the total effect of the force. Impulse applied on an object produces equivalent vector change in its linear momentum also in the resultant direction. The SI unit of impulse N.s or newton second.

Keyterms: Impulse units, Force, Impulsive force, equivalent vector, linear momentum, newton second, constant, motion, momentum, Velocity

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What is Impulse?

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Impulse of force is the product of the resultant force ΣF and the duration of this force Δt if the force is constant. The impulse of force is the cause of changes to motion and therefore changes to momentum. 

Mathematically this can be expressed as:

 ΣF Δt = m (v_final - v_initial) 

Where,

m → Mass of the body 

V_final → Velocity at the end of the time period

V_initial → Velocity at the beginning of the time period. 

Momentum is changed when the mass or velocity of the body changes.

Change in momentum is equal to the product of the average force and time duration and can be expressed as:

J = F_average (t₂ - t₁) 

The impulse is the integral of the resultant force (F) concerning time. 

Force according to Newton's second law

F = dp/dt 

dp = Fdt 

P₁ - P₂ = F × dt 

F × dt = J 

Integrate it over a time interval from t₁ to t₂ 

J = ∫_t1^t2\(\frac {dP} {dt}\)dt

J = ∫_p1^p2 dP

J = P₂ – P₁

J = ΔP

P₁ → initial momentum of the object at t 

P₂ → Final momentum of the object at t

P₂ – P₁ = ΔP = change in momentum during the time interval Δt. 

 It is called the impulse. If the force is constant over the time interval Δt, then 

 J = F × Δt 

Hence the proof. 

Also Read:

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Impulse Formula

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Impulse = Force × (final time - initial time) 

Impulse = Force × Δt

The impulse of the Force = Δt 

I = F × Δt 

The unit of impulse is Newton second, and the dimensionally equivalent unit of momentum is kilogram meter per second. 

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Relation between Momentum and Impulse 

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According to Newton's second law, we know that an unbalanced force always accelerates an object - either by speeding it up or by slowing it down. If the force acts opposite the object's motion, it slows down the object. If the force acts in the same direction as the object's motion then it speeds up the object. 

If the velocity of the object changes then the momentum of the object will also change. Depending on the magnitude of the force and the time the force applied will determine the change in momentum. 

Impulse is a force applied to an object for a certain length of time which will cause the momentum of the object to change. 

Impulse = F x t 

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Impulse - Momentum Theorem 

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The units of impulse can be derived through the impulse-momentum theorem. Impulse Force have a relationship with time, which means Impulse is equivalent to a change in momentum, This can be mathematically written as:

∑→ F Δ t = m Δ → v

The left-hand side of the equation clearly states that force is multiplied by time to give impulse. According to the, SI unit of impulse will be Newton second or N.s.

Here Newton (N) is a derived unit/ compound unit. According to Newton’s second law force can be written as the product of mass and square of velocity that is, 

F = ma =mv²

Expressing the equation in terms of their SI units we get:

N = kg m/s²

On multiplying by s on both sides by we get

N.s = kg \(\frac {m} {s^2}\).s = kg \(\frac {m} {s}\) = kgm /s

Thus, it has the same units and dimensions as momentum

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Application of Impulse Force in Daily Life

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Some of the examples of impulse force that we witness in our everyday lives are as follows:

• Catching a Ball while playing Cricket and hitting a ball with a bat while playing cricket. 
• Airbags of cars are designed based on Impulse.
• Tossing the Coin. 
• Hitting Golf Ball.
• Kick Starting the motorbike, etc. 

Also Read:

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Things to Remember

• Impulsive force is the force applied for a short period of time.
• The SI unit of impulse N.s.
• The units of impulse can be derived through the impulse-momentum theorem.
• Some of the examples of impulse are catching a ball, hitting a ball, tossing a coin etc.
• The dimensionally equivalent unit of momentum and impulse is the same. It can be expressed as Kg.m.s^-1