Momentum Conservation

One of the fundamental laws of the universe that any classical physics simulator, including Universe Sandbox, must follow in order to be able to reproduce realistic motions is the conservation of momentum. Momentum cannot be created nor destroyed, only transferred between objects, so the total momentum of a simulation must remain constant. This is especially important for collisions, in which momentum is exchanged between the colliding objects as they alter each other's velocities.

A similar fundamental law is the conservation of angular momentum: the total angular momentum of a simulation must also remain constant.

Related Properties & Settings

Properties

• The amount of momentum that is lost in the simulation due to the loss of mass (see Limitations) can be seen in the Stats menu in the bottom bar.

Models

Consider an object with mass M₁ and velocity V₁ colliding with another object with mass M₂ and velocity V₂. Before the collision, the total momentum of this simulation is

$P_{initial}=M_{1}V_{1}+M_{2}V_{2}.$

After the collision, the two objects may have new velocities and even new masses, if some of the mass transferred from one body to the other during the collision. Suppose that after the collision, object 1 has mass m₁ and velocity v₁, and object 2 has mass m₂ and velocity v₂. Then the total momentum of the simulation after the collision is

$P_{final}=m_{1}v_{1}+m_{2}v_{2}.$

According to the law of conservation of momentum, momentum cannot be created or destroyed, so the total momentum of the simulation must be the same before and after the collision:

$M_{1}V_{1}+M_{2}V_{2}=m_{1}v_{1}+m_{2}v_{2}.$

Universe Sandbox uses this equation to help calculate what the new velocities, v₁ and v₂, of the objects will be after the collision.

Limitations

Occasionally, mass is lost from the simulation for performance reasons. This lost mass carries with it some momentum, which is therefore also lost from the simulation.