[Alex.Norton]

If you had two identicle systems (wieght, support...) and two wheels that have the same weight but wheel A has less rotational inertia than wheel B, then no, they would spin up to the same speed. However wheel A will take less time to get up to speed than wheel B. However, if you got both wheels up to speed turned off the power, then tried to shoot a ball with the momentum of the wheel (say in 2006), wheel A would shoot fewer balls than wheel B.

In reallity wheel A or gear A would probably also wiegh less, so would put less strain of the system and it might be better balanced which would also reduce stress and so on. So in a real system like a shooter the rotational inertian of the wheel would have a huge effect on the efficiency of the system.

However in a drive train the gears shouldn't be big enough to make a difference. So I will calculate the time it would take the first big gear in the am planetary to spin up. This gear spins at 1540 RPM or 161.26 Radian/sec

m = ~.31kg
w (omega) = 161.26 Radians/sec
I = (mr^2)/2 = 1.562 E-4
T (average) = ~3.95 Nm

in this cas Torque (T) = Moment of Inertia (I) * angular acceleration (a)
so a (alpha) = T/I = 25280 Radians/sec^2

angular velocity (w) = angular acceleration (a) * time (t)
so t = w/a = .00636 seconds

A 120 pound robot (I know its actaully more like 133 lbs) with a reduction of 1:12.75 (AM single speed) to a four inch wheel on the other hand will take:

m = 54.54 kg
F (average) = ~138.04 N
a = F/m = 2.531m/sec^2
vFinal = 2.295 m/s
t = v/a = .907 seconds

So the gear wil take .00636 seconds to spin up and the robot will take .907seconds to accelerate (under absolutely idea situations). There are some assumptions in this. If anyone thinks these assumptions are too extreme, sees a mistake in my math or wants to know where I got a number please PM me.

So since the time of acceleration of the bot is huge compared to the gear it really doesn't make a difference. However you can see that the gear would slow the robot down a little.

In the case of a car there is a much bigger difference because your talking about a 50 lbs fly wheel not a half pound gear. So your theory is correct but I would always sugjest doing to math cause you'll see if you actaully need to think about implimenting it. To do this you should calculate the acceleration of the robot with two different gears (one lightened, one not) and see if there is a difference.

hope that helps
Alex