Pool Ball Collision: Solving for Angular Momentum and Friction

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SUMMARY

The discussion centers on calculating the final speed (V1) and angular speed (W1) of a pool ball after it collides with a wall, given its initial parameters: mass (M), radius (R), initial speed (V0), and initial angular speed (W0). The collision is assumed to be elastic, and the normal force (N) is known. Key equations involve conservation of energy, specifically mV0^2 + Iω0^2 = mV1^2 + Iω1^2, where I is the moment of inertia of the sphere. Participants emphasize the need to account for the effects of friction on angular velocity and the relationship between linear and angular momentum during the collision.

PREREQUISITES
  • Understanding of elastic collisions in physics
  • Knowledge of angular momentum and its conservation
  • Familiarity with the moment of inertia for a sphere
  • Basic principles of friction and its effects on motion
NEXT STEPS
  • Study the conservation of angular momentum in elastic collisions
  • Learn about the moment of inertia calculations for different shapes
  • Explore the effects of friction on angular velocity during collisions
  • Investigate the relationship between linear and angular velocities in rotational dynamics
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Physics students, mechanical engineers, and anyone interested in the dynamics of collisions, particularly in sports physics and mechanical simulations.

  • #31
You have to use Pythagoras
v_{1}=\sqrt{v_{X1}^{2}+v_{Y1}^{2}}
where
v_{Y1}=v_{Y0}=v_{0}sin\alpha_{0} in both cases and v_{X1}, which I counted.
 
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  • #32
Thanks everyone for your help, and thanks Phizyk for the equations. There is something I didn't understand.
\omega is a vector right?
I don't see how to do this comparision v_{X0}<\omega_{0}R+2v_{Y0}\mu{(\frac{mR^{2}}{I}+1) }

Also, It seems weird to me that in the equation v_{X1}=v_{X0}-2\mu{v_{Y0}}, the angular velocity isn't involved in calculation v_{X1}. Is there something I'm missing?
 

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