Double an object’s momentum, and its kinetic energy doesn’t just double. It quadruples. This article covers Newton’s laws, force, and momentum.
General Science
Newton’s Laws, Force and Momentum
The two forces in the Third Law act on different bodies — they don’t cancel out
First Law: Inertia
Rest or uniform motion
More mass means more inertia — resistance to changing motion
Second Law
Force and acceleration
F = ma
Third Law
Action-reaction
Equal and opposite, acting on two different bodies
Momentum
Mass × velocity
Conserved in any collision — powers rocket thrust and gun recoil
✊ Must Know
Newton’s Three Laws and Momentum
- First LawA body stays at rest, or in uniform motion, unless an external force acts on it. This resistance to a change in motion is called inertia, and it depends only on mass — more mass means more inertia.
- Second LawForce equals mass times acceleration, F = ma.
- Third LawEvery action has an equal and opposite reaction, acting on two different bodies.
- MomentumMomentum is the product of mass and velocity. It is conserved in any collision, whenever no external force acts.
- Rockets and RecoilA rocket’s thrust and a gun’s recoil both work on conservation of momentum.
📘 Good to Know
Inertia in Practice, and Impulse
- Inertia in a CarPassengers lean forward when a car stops suddenly, since their bodies, by inertia, tend to keep moving even as the car stops.
- ImpulseImpulse equals the change in momentum. It also equals force multiplied by the time over which it acts.
- Gun RecoilA gun recoils with much less velocity than the bullet, since the gun’s much larger mass needs a smaller velocity to match the bullet’s momentum.
- Comparing MassesGiven several objects, from an atom to a cricket ball, the one with the greatest mass always has the greatest inertia — size and speed don’t matter for this comparison.
Test Yourself
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🌟 Great to Know
Real-World Applications and Momentum-Energy Link
- Third Law, ExplainedNewton’s Third Law can seem to contradict everyday intuition, but the two forces act on different bodies, so they don’t cancel out and prevent motion.
- Buffers and Run-UpsTrain buffers and long-jump run-ups both apply these principles practically, spreading out force over time or building momentum before a jump.
- Rocket PropulsionConservation of momentum underlies rocket propulsion, one of the most important real-world applications of basic Newtonian mechanics.
- Worked ExampleA 10 kg object moving at 10 m/s has momentum 10 × 10 = 100 kg·m/s, and kinetic energy ½ × 10 × 10² = 500 J.
- Why KE QuadruplesKinetic energy relates to momentum as KE = p²/2m. Since KE depends on momentum squared, doubling an object’s momentum quadruples its kinetic energy, not just doubles it.
📝 Exam Point of View
Exam Point of View
- NDA-NA-2 2016Push, friction, and strain (tension) are all contact forces, needing objects to physically touch. Gravity acts across empty space with no contact, so it is the odd one out here. View this question on the full NDA-NA (II) 2016 paper →
- NDA-NA-I 2026, Q75The area under an F-t graph is impulse, not the peak force. Splitting the trapezoid into two triangles and a rectangle gives 400 N·s total, so a 10 kg object starting at rest reaches 40 m/s, not 0, even though the force itself ends back at zero. View this question on the full NDA-NA-I 2026 paper →
- NDA-NA-I 2026, Q70A skydiver falling at a uniform speed has zero acceleration, so the upward drag force must exactly equal the downward weight — 60 kg × 9.8 m/s² = 588 N. View this question on the full NDA-NA-I 2026 paper →
- NDA-NA-I 2026, Q63A soft-sand landing changes the person’s momentum by about the same amount as a hard landing, but stretches the stop over more time, cutting the force by the impulse formula. View this question on the full NDA-NA-I 2026 paper →
- CDS-I 2026, Q11The second law is qualitatively “rate of change of momentum equals applied force” — not angular momentum, displacement, or acceleration, which are common wrong substitutions. View this question on the full CDS-I 2026 paper →
- NDA-NA-I 2026, Q57A particle’s position vector gives velocity with a constant j-component, so force (along i only) can never be parallel to momentum. View this question on the full NDA-NA-I 2026 paper →
- NDA-NA-I 2018, Q56Of an atom, a molecule, a coin, and a cricket ball, the cricket ball has the greatest inertia — mass alone decides it. View this question on the full NDA-NA-I 2018 paper →
- NDA-NA-I 2018, Q58Gravitational force is NOT the same for all pairs of bodies — it depends on both masses and the distance between them, per Newton’s law of gravitation. Test yourself on this question
- CDS-2 2025, Q23Momentum is conserved exactly when the net external force is zero — not when torque or work is at a maximum. View this question on the full CDS-2 2025 paper →
- CDS-II 2022, Q24A direct calculation: 10 kg at 10 m/s gives momentum 100 N·s and kinetic energy 500 J — both formulas applied cleanly. View this question on the full CDS-II 2022 paper →
- CDS-II 2020, Q86Doubling momentum quadruples kinetic energy, since KE scales with momentum squared — a common trap for anyone who assumes a simple doubling. View this question on the full CDS-II 2020 paper →
- The PatternThese questions reward knowing the exact relationship between momentum, force, and energy — not just the definitions in isolation.
- NDA & NA (I) 2025 GAT, Q131Asked the unit of the gravitational constant G. The answer is N-m^2/kg^2, derived directly from rearranging Newton’s law of gravitation. Test yourself on this question
- NDA & NA (II) 2025 GAT, Q54Asked which statement about the second law of motion is wrong. The answer is that force is proportional to momentum — it is actually proportional to the rate of change of momentum, not momentum itself. Test yourself on this question
- NDA & NA (II) 2025 GAT, Q68Asked why a fielder pulls hands back while catching a fast ball. The answer is to reduce the ball’s acceleration, since stretching the stopping time over longer reduces the force needed to change its momentum. Test yourself on this question
Related Topics
- GenSci0001 — Physics Fundamentals for Competitive Exams — the brief introduction to Newton’s laws that this article expands into a full momentum-focused treatment.
- GenSci0012 — Kinematics: Distance, Speed, Velocity and Acceleration — the motion concepts (velocity, acceleration) that this article’s forces act upon.
- CDS-2 2025 GK Paper — contains the momentum-conservation PYQ cited above.
- Browse all General Science articles
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