Theme A — Space, Time and Motion
A.2.13 Force and Momentum — IB Physics HL Revision Notes & Topical Questions
5 min read 10 parts Lesson 24 of 63 1 quiz
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.
Lesson summary
A.2.13 Force and Momentum — IB PHYSICS SL notes: Use F = Δp/Δt, including variable mass and continuous streams, to relate force to the rate of change of momentum.Statement — the resultant force on a body equals the rate of change of its momentum, F = Δp/Δt.What the symbols mean: …
- Change in momentum
- Constant mass
- Direction of F
- Positive direction
- Change of direction
- Mass per second
Part 1 of 8Second law in momentum form
Statement
- Statement the resultant force on a body equals the rate of change of its momentum, 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)
- F is the resultant force in N and Δt the time in s.
Change in momentum
- Δp = pf − pi, in kg m s−1.
Constant mass
- Δp = mΔv, so F = m(Δv/Δt) = ma.
Variable mass
- Variable mass the momentum form still works when mass changes, but F = ma does not.
Meaning
- Meaning a force transfers momentum into or out of a body every second.
Part 2 of 8Direction of force and momentum
Vectors
- Vectors force and momentum both have magnitude and direction.
Direction of F
- Direction of F it is the direction of Δp, not necessarily of the velocity.
Positive direction
- Positive direction it is taken as the direction of the initial motion.
- A force opposing the initial velocity is negative.
Third law
- Third law the force the object exerts on a wall and the force of the wall on the object are equal and opposite.
Change of direction
- Change of direction a ball moving 10 m s−1 east and leaving 10 m s−1 north has Δp = m(vf − vi) of magnitude 10√2 m pointing north-west.
Part 3 of 8Force from a continuous stream
Force from a continuous stream
Mass per second
- F = (Δm/Δt)Δv.
Jet of water
- Jet of water density ρ, area A and speed v deliver mass ρAv each second.
Water stops on a wall
- F = ρAv2.
Water bounces back at the same speed
- Δv is 2v, so F = 2ρAv2.
Other streams
- Other streams hailstones on a roof, bullets from a machine gun, sand on a belt and wind on a sail give steady forces in the same way.
Part 4 of 8Rockets and variable mass
Thrust
- Thrust a rocket expels exhaust at speed ve relative to itself, so F = (Δm/Δt)ve forwards.
Third law
- Third law the exhaust gains momentum backwards and the rocket gains an equal amount forwards.
Acceleration
- Acceleration a = /m, which increases as fuel is used because m decreases.
- (thrust − weight)
In a vacuum
- In a vacuum a rocket works because it pushes against its own exhaust, not the air.
Same approach
- Same approach jet engines and a person holding a hose.
Part 5 of 8Circular motion
Constant speed
- Constant speed the velocity direction changes, so the momentum changes continuously.
Force
- Force the centripetal force towards the centre is the rate of change of momentum.
Part 6 of 8Method
1
Identify the object or mass of fluid whose momentum changes.
2
Write the initial and final momentum as vectors.
3
Find Δp, then divide by the time or use the mass per second.
4
State the direction of the force on the object.
5
Use the third law to give the equal and opposite force on the surface.
- Words to watch
- "from", "acting on" and "exerted on" show which object the force acts on.
Part 7 of 8Link with impulse and kinematics
Impulse
- F = Δp/Δt is the same relation as FΔt = Δp.
Bouncing ball
- Bouncing ball a ball dropped from height h arrives with p = m√(2gh) and rebounds to h′ with p = m√(2gh′).
- The change in momentum is m(√(2gh) + √(2gh′)) for a rebound upwards.
- Dividing by the contact time gives the average force on the floor.
No contact time given
- No contact time given if the ball compresses by a small distance d, the deceleration follows from v2 = 2ad.
Part 8 of 8More from the specification
More from the specification
Newton's Second Law and Momentum Formulation
- Newton's second law states that the resultant force acting on a body equals the time rate of change of linear momentum: F = dp/dt = delta_p / delta_t,
- reducing to F = ma when mass is invariant.
Newton's Third Law and Interaction Pairs
- When two bodies exert contact forces upon one another, the forces are equal in magnitude, opposite in direction,
- and act on different objects along the same line of interaction.
Collisions and Mechanical Energy Dissipation
- While total linear momentum is conserved in all isolated collisions, kinetic energy is conserved exclusively in perfectly elastic collisions;
- in inelastic collisions, energy is dissipated as internal thermal energy.
Circular Motion Dynamics and Centripetal Force
- When an object moves in a horizontal circle of radius r with angular speed omega, a centripetal force F = m omega2 r directed towards the centre is required to sustain the circular trajectory.
Newton's Second Law and Momentum Formulation
- Newton's second law states that the resultant force acting on a body equals the time rate of change of linear momentum: F = dp/dt = delta_p / delta_t,
- reducing to F = ma when mass is invariant.
Newton's Third Law and Interaction Pairs
- When two bodies exert contact forces upon one another, the forces are equal in magnitude, opposite in direction,
- and act on different objects along the same line of interaction.
Collisions and Mechanical Energy Dissipation
- While total linear momentum is conserved in all isolated collisions, kinetic energy is conserved exclusively in perfectly elastic collisions;
- in inelastic collisions, energy is dissipated as internal thermal energy.
Circular Motion Dynamics and Centripetal Force
- When an object moves in a horizontal circle of radius r with angular speed omega, a centripetal force F = m omega2 r directed towards the centre is required to sustain the circular trajectory.
Static friction
- Friction between surfaces at rest relative to each other; fs ≤ μsFN.
Kinetic energy
- K = ½mv2, energy of motion.
Angular speed
- Magnitude of the angular velocity.
Normal reaction
- The contact force perpendicular to a surface.
Reaction force
- Force from a support pushing up on an object.
Friction
- Force parallel to the surface opposing relative motion or its tendency.
Newton
- Unit of force, kg m s-2.
Collision
- Short interaction with large internal forces.
Linear
- A graph that is a straight line through the origin, so resistance is constant.
Radius
- Distance from the centre to the circular path.
Normal
- Line at 90° to a surface.
Tension
- Force transmitted along a string or rope.
Buoyancy
- Another name for upthrust.
Key terms
| Term | Meaning |
|---|---|
| Rate of change of momentum | Change in momentum per unit time, equal to the resultant force |
| Thrust | Force on a rocket from the exhaust it expels, (Δm/Δt)ve |
| Mass flow rate | Mass passing a point per second, ρAv for a stream |
| Resultant force | Vector sum of the forces on a body |
| Variable mass | A system whose mass changes, so F = ma does not apply |
| Change in momentum | Final momentum minus initial momentum, Δp = pf − pi |
Avoid these mistakes
1
Using F = ma when the mass changes — use F = Δp/Δt.
2
Taking the force direction as the velocity direction — it is the direction of Δp.
3
Forgetting the sign change of momentum on rebound — velocity reverses.
4
Using the mass of the whole jet instead of the mass per second — use ρAv.
5
Forgetting the equal and opposite force on the surface — apply the third law.
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