You guys have been a great help so far, and I'm sorry for asking so many questions, (I litterally have thousands) but I have run into a phrase I don't understand in my book.

The book reads as follows:

"Suppose we are told that the accelerationaof a particle moving with uniform speedvin a circle of radiusris proportional to some power ofrsayr^n, and some power ofv, sayv^m. How can we determine the values ofnandm?

Solution:

Let us takeato be

a = k(r^n)(v^m)

wherekis a dimensionless constant of proportionality. Knowing the dimensions ofa,r, andv, we see that the dimensional equation must be

L/TĀ² = (L^n)((L/T)^m= (L^(n+m))/T^m"

I believe I understand all of this to this point, but this next statement confuses me.

"This dimensional equation is balanced under the conditions

n+m= 1 andm= 2

Thereforen= -1, and we can write the acceleration expression as

a=k(r^-1)(v^2) =k/((v^2)/r

When we discuss uniform circular motion later, we shall see thatk= 1 if a consistent set of units is used. The constantkwould not equal 1 if, for example,vwere in km/h and you wantedain m/sĀ²."