Unit Of Force - Derivation Of SI Unit And Other Units - Vedantu

Force is a fundamental concept in physics, describing any interaction that causes an object to change its state of motion. The measurement of force plays a vital role in understanding motion, dynamics, and the effects objects exert on each other. To maintain consistency and clarity in scientific studies and practical applications, a standard unit is used to quantify force.

What is the SI Unit of Force?

The International System of Units (SI) is the globally accepted system for measuring all physical quantities, including force. In this system, the unit of force is called the newton, represented by the symbol N. One newton is formally defined as the amount of force required to accelerate a mass of one kilogram at a rate of one metre per second squared.

Base Units Relevant to Force

To understand the unit of force, consider its three base quantities:

• Metre (m): unit of length
• Kilogram (kg): unit of mass
• Second (s): unit of time

Combining these, a newton can be broken down as:

• 1 N = 1 kg × 1 m/s²

Derivation of Newton as the SI Unit

Force is calculated using Newton’s second law of motion:

• F = m × a
• F = force (in newtons, N)
• m = mass (in kilograms, kg)
• a = acceleration (in m/s²)

This equation means that a force of one newton will accelerate a mass of 1 kilogram by 1 metre/second².

Common Units of Force and Their Conversions

System	Unit Name	Symbol	Relation/Definition	Conversion
SI	Newton	N	Force to accelerate 1 kg by 1 m/s²	—
CGS	Dyne	dyn	Force to accelerate 1 g by 1 cm/s²	1 N = 100,000 dyn
Imperial	Pound-force	lbf	Force to accelerate 1 lb by 32.174 ft/s²	1 lbf ≈ 4.448 N

SI Prefixes and Representation

The SI system supports the use of prefixes to express very large or small forces. For example:

• kN (kilonewton) = 1,000 N
• mN (millinewton) = 0.001 N

This use of prefixes makes it practical to write and interpret values across a wide range of applications.

Stepwise Approach to Force Calculations

1. Identify the mass (m) of the object in kilograms (kg).
2. Determine the acceleration (a) in metres per second squared (m/s²).
3. Apply the formula: F = m × a.
4. Express your answer in newtons (N) using SI units.

Worked Example

Suppose a force acts on a 2 kg object causing it to accelerate at 3 m/s². Calculate the force.

• m = 2 kg
• a = 3 m/s²
• F = m × a = 2 × 3 = 6 N

Therefore, a force of 6 newtons is applied to the object.

Summary Table: Force in SI System

Physical Quantity	Base SI Unit	Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Force	newton	N (= kg·m/s²)

Quick Reference: Key Formula

Formula	Meaning
F = m × a	Force equals mass times acceleration
1 N = 1 kg × 1 m/s²	Unit definition of newton

Explore More on Vedantu

• What is Force?
• Newton’s Laws of Motion
• Force and Acceleration
• Force and Motion
• Work and Energy
• Contact and Non-Contact Forces

By understanding and using the SI unit of force—the newton (N)—students can accurately solve problems in mechanics and related areas. Practice identifying correct units in all calculations to build strong conceptual skills in physics.