Quote:
Originally Posted by Flatlander
Couple things to note:
The total kinetic energy is NOT just it's linear velocity (E=.5*m*v^2) but you must add its rotational energy also (E=.5*I*w^2) where I=moment of inertial and w=angular velocity. So with no way of determining the angular velocity (rate of spin) you can't accurately predict/calculate the total kinetic energy with just a chrony.
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Although, would the rotational Kinetic energy be negligable compared to the linear kinetic energy?
What is the moment of Inertia for a sphere? I'm not entirely sure, but I'm assuming that it'll be similar to the moment of inertia of a circle in which the radius is to the power of four. 6mm (or 0.006m) to the power of four is a much, much smaller number (we are talking about several magnitudes of ten smaller). That probably makes Pi the biggest factor in the equation for angular/rotational energy. The smallest factor in the linear energy equation is mass (0.00025 for .25g BBs), but it is being multiplied by a much bigger number (ie the velocity squared).
Looking at it in that manner, I'd say Angular Energy << Linear Energy.
Quote:
Originally Posted by Flatlander
Momentum has more to do with how hard the bb's will hit (M=m*v) and isn't related to kinetic energy. Obviously a 25% increase in BB weight (.20-.25) does not result in a 25% decrease in velocity, therefore more momentum is present.
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Sure it is. If kinetic Energy is E=(m*v*v)/2 and Momentum is M=m*v then a simple relationship between Momentum and Kinetic energy can be defined consider both rely on the basic measurements of mass and velocity.
Example:
E=(M*v)/2 since M=m*v
So really Kinetic energy is really just momentum multiplied velocity then halved.
It makes sense that these two be related. Obivously as momentum increases you would expect the kinetic energy to increase. Obviously as Veloctiy increases you would expect both to increase. Obviously if the object became heavier you'd expect both the increase.
I agree that an increase in weight won't mean an exact decrease in velocity. Weight is absolute in this case. Aside from removing or chemically changing the composition of the BB, the mass will remain the same throughout the entire trajectory. So to begin with you know the BB is either .20g or .25 g (or what ever weight you want) and that won't change. Velocity is a much more fickle matter. Gun performance/consistancy, air currents/resistance, and all that play a big role in velocity. The effects of one thing or many things could (and most likely does) change depending on the density of the BB used. My guess is that because the velocity of an object moving through a fluid is largely based on it's shape, since the BBs are exactly the same shape, the velocity has a somewhat noticable decrease, but not that which is required to completely balanced to effects of the heavier BB.
Quote:
Originally Posted by Flatlander
I can't comment on any empirical evidence (as I have none) but this is my knowledge of the theory.
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I can't comment on any either (nor do I), but this is my knowledge of basic equation and relationship manipulation.