In physics, Dimensional Analysis is used to express any complex derived physical quantity purely in terms of the seven fundamental base units: Mass [M], Length [L], and Time [T]. One of the most foundational derived quantities in mechanics is Force.
The dimensional formula of Force is [M¹ L¹ T⁻²].
Quantity: Force (F).
Formula Used: Newton's Second Law (F = ma).
Dimensional Formula: [M¹ L¹ T⁻²].
SI Unit: Newton (N).
Base Unit Breakdown: 1 Newton = 1 kg·m/s².
To find the dimension of any quantity, you must start with its fundamental mathematical formula. According to Newton's Second Law of Motion, the formula for Force is: Force = Mass × Acceleration (F = ma)
Let's break this down into base dimensions:
Now, multiply them together: Force = [M] × [L T⁻²] Force = [M¹ L¹ T⁻²]
The standard SI unit of Force is the Newton (N). If we look at our derived dimension [M¹ L¹ T⁻²], we can easily see exactly what a Newton is made of:
The dimensional formula of force is [M L T⁻²].
It is derived using the formula F = ma. We multiply the base dimension of Mass [M] by the derived dimension of Acceleration [L T⁻²] to get [M L T⁻²].
In classical mechanics, all formulas are broken down into three fundamental base dimensions: Mass [M], Length [L], and Time [T].
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