Unit of Force - Definition, Unit, Types, Formula, FAQs

What is the SI Unit of Force?

The International System of Units $(\mathrm{SI})$ is the globally accepted standard for measuring physical quantities such as length, mass, time, and force. In this system, the SI unit of force is called the newton (N), named after Sir Isaac Newton.

One newton is defined as the force required to accelerate a body of mass one kilogram at a rate of one metre per second squared.

$
1 \mathrm{~N}=1 \mathrm{~kg} \times 1 \mathrm{~m} / \mathrm{s}^2
$

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Derivation of SI Unit of Force in Physics

The SI unit of force is derived from Newton's Second Law of Motion. According to this law, force is equal to the product of mass and acceleration and is written as

$
F=m a
$

In the SI system, mass is measured in kilogram (kg) and acceleration is measured in metre per second squared ( $\mathrm{m} \mathrm{s}^{-2}$ ).

Substituting these units in the formula,

$
\begin{aligned}
& \text { Unit of Force }=\mathrm{kg} \times \mathrm{m} \mathrm{~s}^{-2} \\
& \text { Unit of Force }=\mathrm{kg} \mathrm{~m} \mathrm{~s}^{-2}
\end{aligned}
$

This unit, kilogram metre per second squared, is given a special name called Newton (N).
One Newton is defined as the force required to produce an acceleration of $1 \mathrm{~m} \mathrm{~s}^{-2}$ in a body of mass 1 kg .

$
1 N=1 \mathrm{~kg} \mathrm{~m} \mathrm{~s}^{-2}
$

Thus, the SI unit of force is Newton (N).

Other Units of Force

Besides the SI unit newton (N), force is measured in several other units depending on the system of measurement.
1. Dyne (dyn)

• System: CGS (centimetre-gram-second)
• $1 \mathrm{dyn}=10^{-5} \mathrm{~N}$
• One dyne is the force required to accelerate a mass of $\mathbf{1 g r a m}$ by $\mathbf{1 ~ c m} / \mathbf{s}^{\mathbf{2}}$.
• Commonly used in measuring surface tension.

2. Gram-force (gf)

• $\mathbf{1 ~ g f} \boldsymbol{=} \mathbf{0 . 0 0 9 8 ~ N}$
• Force exerted by gravity on a $\mathbf{1}$ gram mass.

3. Poundal (pdl)

• System: FPS (foot-pound-second)
• $\mathbf{1 ~ p d l} \boldsymbol{=} \mathbf{0 . 1 3 8 2} \mathbf{N}$
• Force needed to accelerate $\mathbf{1}$ pound mass by $\mathbf{1 ~ f t} / \mathbf{s}^{\mathbf{2}}$.

4. Pound-force (lbf)

• $\mathbf{1 ~ l b f} \boldsymbol{=} \mathbf{4 . 4 4 8 2 2} \mathbf{~ N}$
• Gravitational force on a 1 pound mass.

5. Kilogram-force (kgf)

• 1 kgf $=9.80665$ N
• Force exerted by gravity on a $\mathbf{1 ~ k g}$ mass.

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