Dimensional Analysis

DIMENSIONAL ANALYSIS

Velocity

Formula	Dimension
v= d/t v – velocity d –distance t –time	d dimension = L t dimension =T è v dimension = [L][T]-1

Acceleration

Formula	Dimension
a = v/t v – velocity t –time	v dimension = [L][T]-1 t dimension =T è a dimension = [L][T]-1[T]-1 = [L][T]-2

Force

Formula	Dimension
F=ma F – Force m - Mass a - Acceleration	m dimension = M a dimension = [L][T]-2 è F dimension = [M][L][T]-2
Or F = mv/t m - Mass v – velocity t – time (in second)	m dimension = M v dimension = [L][T]-1 t dimension = T è F dimension = [M][L][T]-1[T]-1

Momentum

Formula	Dimension
P=mv P - Momentum m – Mass v – velocity	m dimension = M v dimension = [L][T]-1 è P dimension = [M] [L][T]-1

Kinetic Energy

Formula	Dimension
EK = (1/2)mv2 Ek – Kinetic Energy m – Mass v - velocity.	m dimension = M v dimension = [L][T]-1 è EK dimension = [M] [L]2[T]-2

Potential Energy

Formula	Dimension
Ep = m x g x h Ep –Potential Energy m - Mass g – Gravitation h – Height	m dimension = M g dimension = [L][T]-2 h dimension = L è Ep dimension = [M][L][T]-2[L] = [M][L]2[T]-2

Work

Formula	Dimension
W= F x d W - Work F - Force d - distances	F dimension = [M][L][T]-2 d dimension = L è W dimension = [M][L][T]-2[L] = [M][L]2[T]-2

Impulse

Formula	Dimension
I = Favg.∆t I – impulse Favg – Average Force t – time (in second)	F dimension = [M][L][T]-2 t dimension = T è I dimension = [M][L][T]-2[T] = [M][L][T]-1
or I = m∆v m – Mass v –Velocity	m dimension = M v dimension = [L][T]-1 è I dimension = [M][L][T]-1