Section Summary

8.1 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, $F_{\text{net}}=\frac{\text{Δ}p}{\text{Δ}t}$ .
• Impulse is the average net external force multiplied by the time this force acts, and impulse equals the change in momentum, $\text{Δ}p=F_{\text{net}}\text{Δ}t$ .
• Forces are usually not constant over a period of time, so we use the average of the force over the time it acts.

8.2 Conservation of Momentum

• 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.

8.3 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.