# damage=K loss (conserv'n momentum)

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Question for those of you who are familiar with conservation of momentum (and angular momentum). The eq'n for the final velocity of object 1 is: V1f= ( (c+1)M2V2+V1(M1-cM2) ) / (M1+M2) where c is the coefficient of restitution. c, in my game, is the average of the sharpness of the attackers weapon (the lower, the sharper) and the hardness of the defender's armor (the higher, the harder). This is because higher c's make for more deflective blows, where lower c's are more likely to cause kinetic energy loss to U(deformation). as is, V1 is the velocity of the weapon, which is actually a combination of the running velocity of the offender and the linear velocity ( rω ) of the weapon. My question is if this is an OK assertion. I'm unsure of the difference between linear and angular conservation of momentum, and when one is OK to use and not the other. My present equation: V1f= ( (c+1)M2V2+(Vrun+rω)(M1-cM2) ) / (M1+M2) is based on the conservation of linear momentum (right?). Is that ok to use, even though the sword-swinging velocity is angular? If it means anything, ω is a function of torque, derived by: T=Iα α=T/I ω=Tt/I

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yes. one should always use conservation of linear momentum about the center of mass in the absense of external forces.

linear and angular momenta are different beasts and both are conserved seperately. It's a little counter intuitive because you may think that some of the linear momentum is "converted" to angular momentum, but it's not.

This might make more sense if you think that the connection is made between linear/angular because a force may(or may not) have an associated torque and therefore a force (may) have effect on both linear and angular momenta.

Whenever solving combination linear/angular momenta problems it is sometimes useful to choose a non-inertial(i.e., rotating) reference frame. You want to have as many forces as possible to be radial(as opposed to tangential) because radial forces have no associated torques.

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so if I have my character swinging a sword in 3d and hit a mob, the only external force I can think of that would affect momentum conservation would be weight, which woud affect both linear and angular conservation. So can I even use either laws here? If so, should I use BOTH laws, since you said they are different beasts? How should I use these laws?
My present eq'n is
V1f= ( (c+1)M2V2+V1(M1-cM2) ) / (M1+M2)
from linear momentum conservation, derived from pv(i)=pv(f). If angular mom. conserv. is Iω(i)=Iω(f), then can I simply sub it in to the previous eq'n as
ω1f= ( (c+1)I2ω2+ω1(I1-cI2) ) / (I1+I2) ?
And if that's the case, can I use just that equation to determine everything (by converting the mob's final angular velocity to linear)?

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You can use one law or the other or both, depending on what you want at the end result. If you want to have the sword give up a little of both linear and angular momenta to the thing hit by the sword, then you could solve both.

As for external force of weight/gravity, that is why it is useful to calculate momenta in the right reference frame. By calculating with respect to the center of mass, then gravity is only an external force and not an external torque (since gravity acts radially)

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