Linear Momentum, Force, and Impulse
- Linear momentum, often referenced as momentum for short, is defined as the product of a system’s mass multiplied by its velocity, p = mv.
- 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, Fnet=ΔpΔt𝐹net=Δ𝑝Δ𝑡 .
- Impulse is the average net external force multiplied by the time this force acts, and impulse equals the change in momentum, Δp=FnetΔtΔ𝑝=𝐹netΔ𝑡 .
- Forces are usually not constant over a period of time, so we use the average of the force over the time it acts.
Conservation of Momentum
- The law of conservation of momentum is written ptot = constant or ptot = p′tot (isolated system), where ptot 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.
Elastic and Inelastic Collisions
- If kinetic energy is conserved, the collision is elastic. If they stick together, the collision is perfectly 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.
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