# Thread: another math problem in my physics book

1. 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. "Suppose we are told that the acceleration a of a particle moving with uniform speed v in a circle of radius r is proportional to some power of r say r^n, and some power of v, say v^m. How can we determine the values of n and m?

Solution:

Let us take a to be

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

where k is a dimensionless constant of proportionality. Knowing the dimensions of a, r, and v, we see that the dimensional equation must be

L/TÂ² = (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 and m = 2

Therefore n = -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 that k = 1 if a consistent set of units is used. The constant k would not equal 1 if, for example, v were in km/h and you wanted a in m/sÂ²."  2.

3. Nevermind, I see. I should have seen it before. L/TÂ² = (L^(n + m))/T^m

so 1 = n + m and 2 = m

thus n = -1  Bookmarks
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