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What does sub i mean?

by The riddler
Tags: derivitive, equation, kinetic energy, time
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The riddler
Jul2-10, 03:03 AM
P: 94
Im not 100% sure what the "sub i" symbol means when next to values such as Velcoity and Aceleration, here is and example of it being used in this equation for the time derivitive of kinetic energy.

Ek(d/dt) = Σm*Vi*Ai

Ek = Kinetic energy
d = Derivitive
t = Time
V = Velocity
A = Acceleration
sub i = ???

Can someone please tell me what it stands for,

Thanks for any replies :)
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Jul2-10, 03:11 AM
PF Gold
Pengwuino's Avatar
P: 7,120
The subscript 'i' refers to the component x,y, and z. It is an index that goes from 1 to 3, 1 = x, 2 = y, 3 = z that is used for the sum. In this case, it means the sum of [tex]mV_x A_x + mV_y A_y + mV_z A_z[/tex] in component terms.

In more advanced studies, you'll see the summation term dropped and when you see a repeated index such as the one you have, that kind of sum is implied. On the other hand, if you have something like [tex]A_i B_j[/tex] where A and B are just two indices, the index runs from 1 to 3 on both i and j so you get 9 terms that include [tex]A_1 B_3 , A_2 B_3 , A_1 B_1 [/tex] etc etc.

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