Spin created due to an Elastic Collision of two solid balls

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Discussion Overview

The discussion revolves around the mechanics of elastic collisions between two solid balls, specifically focusing on the calculation of momentum and kinetic energy associated with induced spin. Participants explore the implications of friction and tangential forces in the context of conservation laws in physics.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents equations for angular velocity and asks for the momentum and kinetic energy related to spin in an elastic collision scenario.
  • Another participant questions the possibility of inducing spin without friction, suggesting that tangential forces are necessary for spin generation.
  • A later reply emphasizes that while there may be no energy loss due to friction, friction itself is still required to induce spin, challenging the initial premise of the discussion.
  • One participant clarifies that their focus is on the conservation of kinetic energy and seeks equations that account for the frictional effects that contribute to spin.

Areas of Agreement / Disagreement

Participants express disagreement regarding the role of friction in inducing spin during elastic collisions. Some argue that friction is necessary, while others suggest that energy can be conserved without it, leading to an unresolved discussion on this topic.

Contextual Notes

There are limitations in the assumptions made about friction and its role in the dynamics of the collision, as well as potential dependencies on the definitions of spin and energy conservation in this context.

Philosophaie
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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)
 
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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. :smile:
 
berkeman said:
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. :smile:
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.
 
Philosophaie said:
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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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.
 

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