Question

I just started the first Lecture of professor Lewins, but english is not my first language, so if anyone could help me a bit.. when he is talking about the time it takes for the apple to fall, he show us the equation
[T]¹ = [L]^α . [M]^β . [g(accel)]^γ
then he says something about how
β = 0
α+γ=0
1=-2γ
α=1/2

I just couldn't understand his comment on why β = 0 and α+γ=0.. did I miss something he said or is it just basic physics knowledge I lack on this particular thought?

Answer 1

He's merely comparing the two sides of the equation [T]¹ = [L]^α * [M]^β * [L/T^2]^γ and looking at if the dimensions are there on both sides, and if so, the powers have to be equal.

As he states earlier, "you cannot have coconuts on one side and oranges on the other"--in other words, you need to have everything together on the left side equal everything together on the right side. Keeping this in mind, I will go through two examples:

On the right-hand side of the equation, you have some mass dimension, [M], to the power β . There is no [M] on the left-hand side. Therefore β must equal 0. (As you probably know, anything to the zeroth power is one and one times anything is that other number.)

There is no [L] on the left side but on the right side you have [L]^α and [L]^γ. The left side essentially could be written as [L]^0. So the exponents on the left for [L] must equal the exponents on the right, α and γ. In other words, 0 = α + γ.

Hopefully if you watch the video again now, you should be able to figure out the rest of the problem by yourself. Let me know if you still need help.

Answer 2

aahhh I understand now.. thank you my friend! (:

Answer 3

You're welcome! :)