Please i want explanation of dimensional analysis

[Andy6]

 

[PeterO]

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.