Can Angular Momentum Equations Be Adapted from Linear Momentum Formulas?

[lefnire]

using the conservation of linear momentum with a known coefficient of restitution (COR), one can obtain the final velocity of object 1 with this eq'n:

V1,f= [U](COR+1)M2V2-V1(M1-COR*M2)[/U]
               M1+M2

conservation of linear momentum looks like 'mv', where conservation of angular momentum looks like 'Iω'. Based on this, can I sub in 'I' for every 'm' and 'ω' for every 'v' in the previous equation, such that

ω1,f= [U](COR+1)I2ω2-ω1(I1-COR*I2)[/U]
               I1+I2

?

 

[topsquark]

using the conservation of linear momentum with a known coefficient of restitution (COR), one can obtain the final velocity of object 1 with this eq'n:

V1,f= [U](COR+1)M2V2-V1(M1-COR*M2)[/U]
               M1+M2

conservation of linear momentum looks like 'mv', where conservation of angular momentum looks like 'Iω'. Based on this, can I sub in 'I' for every 'm' and 'ω' for every 'v' in the previous equation, such that

ω1,f= [U](COR+1)I2ω2-ω1(I1-COR*I2)[/U]
               I1+I2

?

I will go so far as to answer this question with a "yes," but have some care.

It all depends on how you define the COR. Obviously, the COR associated with the linear problem will not be the same as the COR associated with the rotational problem...

-Dan

 

[charng]

Yes, you can substitute the moment of inertia (I) for mass (m) and angular velocity (ω) for linear velocity (v) in the equation for conservation of linear momentum. This is because both linear momentum and angular momentum are conserved quantities, meaning that they do not change in a closed system. Therefore, the same principles and equations can be applied to both types of momentum.