Question

For a 2D physics simulation, I need to resolve collisions between two objects in 2D. I have available each object's initial angular velocity, linear velocity, mass, moment of inertia, and center of mass. For the collision, I have available the point of contact and coefficient of restitution. How do I calculate each object's final angular and linear velocity?

Answer 1

To calculate the final angular and linear velocity of each object in a 2D collision, you can use conservation of angular momentum and conservation of kinetic energy.

Step-by-step explanation:

To calculate the final angular and linear velocity of each object in a 2D collision, you can use conservation of angular momentum and conservation of kinetic energy. Conservation of angular momentum states that the initial angular momentum before the collision is equal to the final angular momentum after the collision. You can use the equation I₁w₁ + I₂w₂ = I₁w'₁ + I₂w'₂, where I is the moment of inertia and w is the angular velocity. By rearranging the equation, you can solve for the final angular velocities w'₁ and w'₂.

Conservation of kinetic energy states that the initial kinetic energy before the collision is equal to the final kinetic energy after the collision. You can use the equation 0.5m₁v₁² + 0.5m₂v₂² = 0.5m₁(v'₁)² + 0.5m₂(v'₂)², where m is the mass and v is the linear velocity. By rearranging the equation, you can solve for the final linear velocities v'₁ and v'₂.