Sections

Section Summary
# Section Summary

- Linear momentum, often referenced as
*momentum*for short, is defined as the product of a system’s mass multiplied by its velocity,**p**=*m***v**. - The SI unit for momentum is kg m/s.
- Newton’s second law of motion in terms of momentum states that the net external force equals the change in momentum of a system divided by the time over which it changes, ${F}_{\text{net}}=\frac{\text{\Delta}p}{\text{\Delta}t}$.
- Impulse is the average net external force multiplied by the time this force acts, and impulse equals the change in momentum, $\text{\Delta}p={F}_{\text{net}}\text{\Delta}t$.
- Forces are usually not constant over a period of time, so we use the average of the force over the time it acts.

- The law of conservation of momentum is written
**p**_{tot}= constant or**p**_{tot}=**p**′_{tot}(isolated system), where**p**_{tot}is the initial total momentum and**p**′_{tot}is the total momentum some time later. - In an isolated system, the net external force is zero.
- Conservation of momentum applies only when the net external force is zero, within the defined system.

- If objects separate after impact, the collision is elastic; If they stick together, the collision is inelastic.
- Kinetic energy is conserved in an elastic collision, but not in an inelastic collision.
- The approach to two-dimensional collisions is to choose a convenient coordinate system and break the motion into components along perpendicular axes. Choose a coordinate system with the
*x*-axis parallel to the velocity of the incoming particle. - Two-dimensional collisions of point masses, where mass 2 is initially at rest, conserve momentum along the initial direction of mass 1, or the
*x*-axis, and along the direction perpendicular to the initial direction, or the*y*-axis. - Point masses are structureless particles that cannot spin.