Lesson 4 of 6 · Momentum and recoil
Follow momentum through collisions and recoil
9 minute lesson · 3 checks along the way
Your goal for this lessonUse signed momentum to predict a simple collision and explain recoil without assuming kinetic energy is always conserved.
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Keep the direction in the calculation
is mass multiplied by velocity: p = mv. Unlike , it includes direction. Choose one inertial reference frame and, for a straight-line problem, a positive direction. A 2-kilogram object traveling at +3 m/s has momentum +6 kg m/s. Another identical object traveling at −3 m/s has momentum −6 kg m/s. Their total momentum is zero, although their total kinetic energy is positive.
An external force changes a system’s total momentum. Its is the accumulated force over time; for a constant force, impulse equals force times duration. A modest force acting longer can produce the same momentum change as a larger force acting briefly. Conservation of total momentum applies when the chosen system experiences negligible net external impulse over the interval being studied.
Separate internal interactions from outside pushes
Two objects pushing on one another experience equal and opposite forces. These forces change each object’s momentum, while canceling in the sum for the combined system. They do not cancel on either individual object. A spring separating two initially stationary spacecraft can give them opposite momenta. The lighter spacecraft then travels faster in that original frame because equal momentum magnitudes do not imply equal speeds.
For a rocket, include expelled propellant when making this complete-system argument. The remaining spacecraft by itself exchanges momentum with material leaving it. For a collision, distinguish momentum from kinetic energy: momentum can be conserved while deformation and internal heating reduce macroscopic kinetic energy. Energy conservation still holds when the additional forms are counted. These are different conservation statements with different bookkeeping.
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Work through a decision
Solve a gentle model collision
Imagine two nonrotating test carts moving along a frictionless straight track. In the track frame, a 2-kilogram cart travels at +3 m/s and a 4-kilogram cart is stationary. They meet and latch together without ejecting material. Neglect external impulse during contact. Initial momentum is +6 kg m/s. The combined mass is 6 kilograms, so the final velocity is +1 m/s.
Initial kinetic energy is ½ × 2 × 3² = 9 . Final kinetic energy is ½ × 6 × 1² = 3 joules. The 6-joule difference becomes in this ideal enclosed collision. Using conservation of kinetic energy to solve this sticking collision would give the wrong answer. Momentum determines the shared final velocity under the specified conditions, while the energy balance describes the accompanying transformation.
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Why an asteroid impact needs a larger account
DART struck Dimorphos in 2022 to test asteroid deflection. The companion LICIACube recorded material leaving the impact region. That carried momentum, and the asteroid remnant recoiled in response. A model that treats the event as a projectile simply sticking without any material leaving misses an important contribution. Researchers used orbital measurements and impact evidence to investigate the change, not just the brightness of the debris.
The short impact interval can be analyzed with a suitable negligible-external-impulse approximation, while later orbital motion still involves gravity from Didymos and other bodies. The system and time interval must therefore remain explicit. The two-panel image supplies evidence of the aftermath and escaping material. Converting that evidence into a momentum estimate requires masses, velocities, viewing geometry, and uncertainties beyond what either frame alone supplies.
A mission-produced two-panel presentation of LICIACube observations after DART struck Dimorphos on September 26, 2022. Didymos appears above the smaller, debris-surrounded target in each panel. The source already combines two observations; they are not two different asteroid systems in one simultaneous camera frame.
Look closely
Compare the diffuse material around the smaller object in the two panels. What must a momentum model include beyond the incoming DART spacecraft and a single unchanged asteroid?
See what to notice
Expelled material carries momentum, and the remnant recoils. A quantitative model needs the mass and velocity distribution of ejecta, the target properties, and orbital evidence. The brightness and projected shapes alone do not determine the momentum transferred.
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Put it together
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