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In an Elastic Collision in free space with no gravity or friction of two solid balls of radius r1 and r2 I need to calculate the momentum and kinetic energy of the induced spin with angular velocity w1 and w2 to solve for the Conservation of Momentum and Kinetic Energy.

Spin

Angular Velocity

w1 = (v1f-v1i)/r1

w2 = (v2f-v2i)/r2

Spin Momentum

p3f(due to w1) = ?

p4f(due to w2) = ?

Spin Kinetic Energy

KE(due to w1)=?

KE(due to w2) = ?

Conservation of Momentum

m1*v1i + m2*v2i = m1*v1f + m2*v2f + p3(due to w1) +p4(due to w2)

Conservation of Kinetic Energy

1/2*m1*v1i^2 + 1/2*m2*v2i^2 = 1/2*m1*v1f^2 + 1/2*m2*v2f^2+ KE(due to w1)+ KE(due to w2)

Spin

Angular Velocity

w1 = (v1f-v1i)/r1

w2 = (v2f-v2i)/r2

Spin Momentum

p3f(due to w1) = ?

p4f(due to w2) = ?

Spin Kinetic Energy

KE(due to w1)=?

KE(due to w2) = ?

Conservation of Momentum

m1*v1i + m2*v2i = m1*v1f + m2*v2f + p3(due to w1) +p4(due to w2)

Conservation of Kinetic Energy

1/2*m1*v1i^2 + 1/2*m2*v2i^2 = 1/2*m1*v1f^2 + 1/2*m2*v2f^2+ KE(due to w1)+ KE(due to w2)

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