# Dimensional analysis question

## Homework Statement

determin the dimensions of $$\alpha$$ in the following
a)Sin($$\alpha$$X$$^{}2$$) (alpha* X squared) (X is a distance)
b)10$$\alpha$$t3
c)cot($$\alpha$$X2/R) (R is a radius)
d)e(hf/$$\alpha$$T - 1 (h is plancks constant with units J*s) ( f is frequency

## The Attempt at a Solution

so are these all supposed to be dimensionless?

attempt at a: [L2 $$\alpha$$ ] = 1 therefore $$\alpha$$= [1/L2 ] (where L is length)

id appreciate some help :)

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Yes, you're right and the solution is correct. All of those example functions must have dimensionless arguments, otherwise they don't make sense, sort of "apples plus oranges = peaches" or something like that.

just to clarify for b & d, does it matter that the dimensions are in the exponent?

anyone?

tiny-tim
Homework Helper
Hi mjolnir80! (have an alpha: α and a squared: ² and a cubed: ³ )
just to clarify for b & d, does it matter that the dimensions are in the exponent?
No, it's all the same … 10αt³ and sin(αt³) need the αt³ to be dimensionless for exactly the same reason. one more quick thing about dimensional analysis :)
in an equation lets say X=Vit + 1/2 a t2

if we wanted to prove that this equation is dimensionally correct, how would the + between the 2 terms on the r.h.s effect the analysis would we have to ignore the + and just try to make it so that the overall dimensions canel each other out to give lenghth?

tiny-tim
Homework Helper
in an equation lets say X=Vit + 1/2 a t2

if we wanted to prove that this equation is dimensionally correct, how would the + between the 2 terms on the r.h.s effect the analysis would we have to ignore the + and just try to make it so that the overall dimensions canel each other out to give lenghth?
Hi mjolnir80! No … with one or more +s, each part must have the same dimensions …

in this case, X must have the same dimensions as Vit and as 1/2 a t2 