# Spin created due to an Elastic Collision of two solid balls

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)

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berkeman
Mentor
How can you have any change of spin with no friction?

Also, is this for schoolwork? I can move it to the schoolwork forums if it is. How can you have any change of spin with no friction?

Also, is this for schoolwork? I can move it to the schoolwork forums if it is. This is not for schoolwork. In this example there is no loss due to friction. Not sure what friction on the surface is needed to induce a spin. The spin should be a sine function of how far from the Head-On Collision is of the given collision.

jbriggs444
Homework Helper
2019 Award
In this example there is no loss due to friction
No [energy] loss due to friction is not the same thing as no friction. If you want to induce spin on a ball, you need to apply a tangential force. For a spherical ball of uniform density, that pretty much means "friction".

Edit: To see friction in action with [nearly] elastic collisions, bounce a hard but sticky rubber ball on a hard surface with spin and watch the succession of bounces. To get a high initial spin rate, try bouncing the ball on the floor near a wall. The ball picks up spin at the floor, maintains the spin as it strikes low on the wall and then bounces in a crazy fashion back and forth alternating its spin direction each time it strikes the floor. Check out the following at about 49 seconds in.

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• Yan_Dalton and berkeman
What I am saying in the question is there is no loss of energy due to heat loss or other losses. The total "friction" is transferred directly to the spin as in the Conservation of Kinetic Energy equation above. What I want to know is the equation for Momentum and Kinetic Energy due to the "friction" to produce a given spin on each ball.