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Theme A — Space, Time and Motion

A.2.11 Conservation of Linear Momentum — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 22 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

A.2.11 Conservation of Linear Momentum — IB PHYSICS SL notes: Define linear momentum, state the principle of conservation of momentum for isolated systems and apply it to interactions.Linear momentum = the product of mass and velocity, p = mv.p is in kg m s−1, equivalent to N s.m…

  • Sign convention
  • Frame dependence
  • Different bodies
  • Total momentum
  • Opposite vectors
  • Stationary object

Part 1 of 7Linear momentum

Linear momentum
Linear momentum the product of mass and velocity, p = mv.
  • p is in kg m s−1, equivalent to N s.
  • m is in kg and v in m s−1.
Vector
  • Vector it points in the direction of the velocity, so in one dimension the sign shows the direction.
Sign convention
  • Sign convention the initial direction of motion is usually taken as positive.
Rebound
  • Rebound a 60 g ball at 2 m s−1 has p = 0.12 kg m s−1; rebounding at the same speed gives p = −0.12 kg m s−1.
Frame dependence
  • Frame dependence momentum depends on the frame of reference, as velocity does.
Different bodies
  • Different bodies a heavy slow object and a light fast object can have the same momentum.

Part 2 of 7The principle of conservation

The principle of conservation
Principle
  • Principle the total linear momentum before an interaction equals the total after it, unless a resultant external force acts on the system.
Isolated system
  • Isolated system one with no resultant external force.
Total momentum
  • Total momentum it is the vector sum of the momenta of every object.
Opposite vectors
  • Opposite vectors they can cancel, giving a net momentum of zero.
Rebound
  • Rebound an object that rebounds has positive velocity before and negative after.
Stationary object
  • Stationary object it has zero momentum.

Part 3 of 7Why momentum is conserved

Third law
  • Third law the forces on two interacting objects are equal and opposite.
Same time
  • Same time the forces act for the same time, so the impulses are equal and opposite.
Result
  • ΔpA = −ΔpB, so the total is unchanged.
Internal forces
  • Internal forces they cannot change the total momentum, only transfer it between objects.

Part 4 of 7Applying the principle

1
Define the system and check that external forces are negligible during the short interaction.
2
Draw a before-and-after sketch and label all masses and velocities.
3
Choose a positive direction and write each momentum with its sign.
4
Equate the totals: Σmv before = Σmv after.
5
Solve for the unknown velocity or mass.
Two objects
  • Two objects m1u1 + m2u2 = m1v1 + m2v2, where u is the initial and v the final velocity.
Stick together
  • Stick together set v1 = v2 = v to give the common velocity.

Part 5 of 7Collisions and explosions

Collision
  • Collision two bodies exert large forces for a short time, so friction is negligible during contact.
Explosion or recoil
  • Explosion or recoil a stationary system splits and the total momentum stays zero.
  • Examples are a gun and bullet, a person stepping off a boat and a cart launching a ball.
Light piece
  • Light piece it gets the higher speed because m1v1 = −m2v2.
Rocket
  • Rocket it accelerates by throwing exhaust backwards, conserving momentum.
Examples
  • Examples a bowling ball hits a pin that flies off fast while the ball slows a little;
    • a cannon recoils slower than its shell because of its greater mass.

Part 6 of 7Limits and links

Energy
  • Energy momentum is conserved in every isolated collision even when kinetic energy is not.
Single object
  • Single object momentum is not conserved for one object alone,
    • since external forces change it (F = Δp/Δt).
      What the symbols mean: F = force (N) · Δt = time the force acts (s) · Δp = change in momentum (kg m s−1); FΔt is the impulse (N s)
Earth and ball
  • Earth and ball the total momentum of ball plus Earth is conserved when a ball falls.
Vector law
  • Vector law it applies in each perpendicular direction independently, which is how two-dimensional collisions are solved.

Part 7 of 7More from the specification

More from the specification
Newton's third law in collisions
  • Newton's third law in collisions interacting bodies exert equal and opposite forces over identical time intervals, conserving total linear momentum.
Centripetal force in circular motion
  • Centripetal force in circular motion maintaining circular motion along radius r at constant angular speed requires an inward centripetal force.
Momentum conservation against fluid friction
  • Momentum conservation against fluid friction in isolated systems without external fluid drag, vector momentum remains strictly constant before and after collisions.
Conservation of Linear Momentum
  • In an isolated system with no external resultant forces, total linear momentum remains constant before and after collisions or explosions.
    • (m1*u1 + m2*u2 = m1*v1 + m2*v2)
Newton's Third Law and Action-Reaction Pairs
  • When one body exerts a force on a second body, the second body exerts an equal magnitude force in the opposite direction on the first body,
  • forming a Newton third-law pair.
Centripetal Force in Circular Motion
  • For an object moving along a circular path of radius r with constant angular speed omega, centripetal acceleration is given by a = omega2 * r = v2 / r, requiring an inward resultant force.
Motion in a Vertical Circle
  • In a vertical circular trajectory, the net centripetal force at the top is provided by the sum of downward tension and the object's weight, dictating the minimum speed required to maintain circular motion.
Buoyancy
  • Another name for upthrust.
Centripetal force
  • Net force toward the centre, mv2/r.
Static friction
  • Friction between surfaces at rest relative to each other; fs ≤ μsFN.
Angular speed
  • Magnitude of the angular velocity.
Centripetal acceleration
  • Ac = v2/r toward the centre.
Normal reaction
  • The contact force perpendicular to a surface.
Reaction force
  • Force from a support pushing up on an object.
Fluid resistance
  • Drag force from a fluid opposing motion.
Newton
  • Unit of force, kg m s-2.
Weight
  • Gravitational force on a mass.
Constant
  • Not changing.
Radius
  • Distance from the centre to the circular path.
Normal
  • Line at 90° to a surface.
Tension
  • Force transmitted along a string or rope.

Key terms

TermMeaning
Linear momentumProduct of mass and velocity, p = mv; a vector
Conservation of momentumTotal momentum is constant when no resultant external force acts
Isolated systemSystem on which no resultant external force acts
RecoilBackward motion of a body as it expels another part, conserving momentum
Internal forceForce between parts of a system that cannot change its total momentum
Common velocityVelocity of two bodies after they stick together

Avoid these mistakes

1
Forgetting the sign of momentum after a rebound — a reversed velocity makes the momentum negative.
2
Applying conservation when a resultant external force acts — the system must be isolated.
3
Using the speeds instead of the velocities — use signed velocities.
4
Treating the stationary object as having momentum — its momentum is zero.
5
Assuming kinetic energy is conserved because momentum is — only in elastic collisions.

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