Elastic Collisions in Two Dimensions: Oblique Collisions of Spheres

Elastic Collisions in Two Dimensions: Oblique Collisions of Spheres

Fundamentals of Elastic Collisions in 2D: Oblique Collisions of Spheres

• In elastic collisions between spheres, two rules are followed: Conservation of Momentum in both the line of centers and perpendicular to it, and Conservation of Kinetic Energy.

• The coefficient of restitution (e), representing the amount of bounce in the collision, is by definition equal to one in elastic collisions.

Velocity and Angular Velocity Post-Collision

• After the collision, the final velocites of the two spheres can be obtained by applying the principles of conservation of linear momentum and kinetic energy.

• As spheres are three-dimensional bodies, the collision can also spin them about an axis, causing angular velocity.

Mathematical Approach to Elastic Collisions

• The geometry of the collision is crucial in deriving the equations. Knowing the initial velocities and the angle of collision helps in resolving the velocities in the line of centers and perpendicular to it.

• These velocities, along with the masses, are used to apply Conservation of momentum and kinetic energy to derive the final velocities.

Experimental Understanding through Billiards and Snooker

• Billiard and Snooker games can be used as practical real-world examples to understand these complex interactions in two dimensions.

• Impulse, momentum transfer, spin caused by collision and the resulting trajectory of balls can be observed and analyzed.