Please i want explanation of dimensional analysis

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Dimensional analysis involves examining the units in a formula and reducing them to fundamental dimensions such as mass (kg), length (m), and time (s). For example, in the equation F = ma, mass has the dimension of [MASS] and acceleration has dimensions of [LEN][TIME]^-2, leading to force having dimensions of [MASS][LEN][TIME]^-2. Similarly, work is calculated as force multiplied by distance, resulting in dimensions of [MASS][LEN]^2[TIME]^-2. Impulse and momentum share dimensions of [MASS][LEN][TIME]^-1, highlighting their relationship. Numbers in formulas, like the coefficient in P = 4L, are dimensionless and do not affect dimensional analysis.
Andy6
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Andy6 said:

Homework Statement


Homework Equations


The Attempt at a Solution


Dimensional analysis is considering the units of each part of an expression/formula and reducing them to the base references: kg, m, s or [MASS],[LEN],[TIME]

eg F = ma
we know the dimension of the m is [MASS]
we know the dimensions of the a are [LEN][TIME]-2

so hopefully the dimensions of force are: [MASS][LEN][TIME]-2
[they are!]

From there we can Work
[Force * distance] → [MASS][LEN][TIME]-2*[LEN]
Work → [MASS][LEN]2[TIME]-2

Impulse: Force * time → [MASS][LEN][TIME]-2*[TIME]
→ [MASS][LEN][TIME]-1

Momentum: mass*velocity → kg*m/s → [MASS][LEN][TIME]-1

It is nice that Impulse and momentum have the same dimensions!

EDIT: when a number appears in a formula - it has no dimension and is ignored. Take the perimeter of a square P = 4L both perimeter and side length have dimensions [LEN]; we don't have a 4 in there.
 

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