As per the second law of motion proposed by Newton, force is defined or expressed as the product of mass and acceleration.
In both the SI system (the International System of Units) and in MKS system, the unit of mass is kilogram, abbreviated as kg, and the unit of acceleration is m/s². Therefore, the unit of force is kg m/s², which is what we refer to as Newton or N.
In the CGS system of units, the unit of mass is gram or g, and the unit of acceleration is cm/s². Therefore, the CGS unit of force is g cm/s², which is called dyne or Dyn.
In the FPS system of units, the unit of mass is pound or lb, and the unit of acceleration is feet per second squared or ft/s².
Therefore, the FPS unit of force is lb-ft/s², which is called poundal or pdl.
Derivation of SI Unit of Force:
From Newton’s Second Law of motion, force is equal to the rate of change in momentum (P).
We also know that momentum (P) is the product of mass(m) and velocity(v)
Force = Rate of change of momentum
= P/ t {where P stands for momentum and t for time}
= mv/ t { P= mv}
Force= mass*velocity / time -- (replacing terms with their respective units)
Newton = (kg*m)/sec⁻²
Where,
Unit of Force = Newton
Unit of mass = Kilogram
Unit of time = Second
Unit of velocity = Metre / Second
[NOTE: Velocity is Displacement by time. Displacement is the shortest distance from the initial to the final point. In short, displacement is distance in vector form (same as how velocity is speed in vector form), so displacement is measured in metres.]
Other Units of Force:
There are two other units of force in Physics; however, they are not as commonly used as the SI unit of force Newton.
Dyne: A dyne is a force required to give a mass of 1 gram (1 g) an acceleration of 1 centimetre per second squared (1 cm/s²). 1 N = 100,000 dynes. You might use the dyne if you are working with very small objects.
Poundal and Pound: A poundal is a force required to give a mass of 1 pound (1 lb) an acceleration of 1 foot per second squared (1 ft/s²). 1 poundal = 0.1382 N. A pound is a force applied on a mass of 1 pound (1 lb) by the acceleration due to gravity, that is, g. It is a non-technical unit of force and is also referred to as the weight. These units of force are in the English system and are rarely used in scientific measurements.
Gram Force: It is defined as the force of standard gravity on a gram, that is, acceleration due to gravity (g)*gram.
Pond: It is another term for the gram force.
Sthene: It is defined as a tonne meter per second squared.
Ounce-force: An ounce-force is defined as the force of gravity on an avoirdupois ounce (mass = 1 ounce), that is, acceleration due to gravity (g)*ounce.
Ton-force: A Ton-force is defined as the force of standard gravity on 1 ton, that is, acceleration due to gravity (g)*ton.
8. Kip or Kipf: A Kip or Kipf is defined as 1000 pound forces.
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