Spin created due to an Elastic Collision of two solid balls

In summary, to calculate the momentum and kinetic energy of the induced spin with angular velocity w1 and w2 in an elastic collision between two solid balls of radius r1 and r2 in free space with no gravity or friction, you can use the equations w1 = (v1f-v1i)/r1 and w2 = (v2f-v2i)/r2 for angular velocity, p3f(due to w1) = ? and p4f(due to w2) = ? for spin momentum, KE(due to w1)=? and KE(due to w2) = ? for spin kinetic energy, m1*v1i + m2*v2i = m1*v1f
  • #1
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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  • #2
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:
 
  • #3
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.
 
  • #4
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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  • #5
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.
 

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

1. What is spin in the context of an elastic collision between two solid balls?

Spin is a type of rotational motion that occurs when two solid balls collide in an elastic collision. It is the result of the transfer of angular momentum between the two balls during the collision.

2. How is spin created in an elastic collision between two solid balls?

Spin is created when the two solid balls collide and transfer angular momentum to each other. This transfer of momentum causes the balls to rotate around their own axes, resulting in spin.

3. Is the spin created in an elastic collision between two solid balls always the same?

No, the amount of spin created in an elastic collision between two solid balls can vary depending on factors such as the mass and velocity of the balls, as well as the angle of collision.

4. Can spin be observed in an elastic collision between two solid balls?

Yes, spin can be observed in an elastic collision between two solid balls by closely observing the motion of the balls after the collision. The balls will exhibit rotational motion, indicating the presence of spin.

5. What is the significance of spin in an elastic collision between two solid balls?

The presence of spin in an elastic collision between two solid balls is significant because it provides additional information about the collision, such as the direction and magnitude of the angular momentum transferred between the balls. It also affects the final velocities and trajectories of the balls after the collision.

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