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Thread: another math problem in my physics book

  1. #1 another math problem in my physics book 
    Forum Bachelors Degree Demen Tolden's Avatar
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    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 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/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 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/sĀ²."


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  3. #2  
    Forum Bachelors Degree Demen Tolden's Avatar
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    Nevermind, I see. I should have seen it before.

    L/TĀ² = (L^(n + m))/T^m

    so 1 = n + m and 2 = m

    thus n = -1


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