كيف يحسب الرقم الهيدروجيني pH للمحاليل؟ How to calculate pH and pOH?

يحسب الرقم الهيدروجيني بالعلاقة: pH = -log[H⁺]، وللمحاليل المائية عند 25°C: pH + pOH = 14. إذا كان pH 7 فالمحلول قاعدي. [الصيغة الرمزية الموزونة: pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴]

Theme A — Space, Time and Motion

A.2 Forces and Momentum — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 11 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision

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 Forces and Momentum — IB PHYSICS HL notes: Apply Newton's laws, types of force, momentum, impulse, collisions and circular motion to problems of force and motion.A free-body diagram shows all the forces on one object, drawn as arrows from a point mass at the centre of mass.Ar…

Common forces
Resultant (net) force
Second law
What the symbols mean
Contact forces act between touching objects
Use the symbol given in the question

Part 1 of 8Free-body diagrams and resultant force

A free-body diagram shows all the forces on one object, drawn as arrows from a point mass at the centre of mass.

Arrow length shows magnitude and direction shows the direction of the force.
Label each force by name or symbol and include only forces acting on the object.

Common forces

Common forces weight F_g , tension F_T (away from the mass), normal reaction F_N (perpendicular to the surface) and friction F_f (opposite to motion).
- (towards the planet)

Resultant (net) force

Resultant (net) force the vector sum of the forces on a body.

Balanced forces give zero resultant; unbalanced forces give a non-zero resultant.
In one dimension add forces with signs; in two dimensions resolve with Pythagoras and trigonometry.

Part 2 of 8Newton's laws of motion

First law

First law a body stays at rest or moves with constant velocity unless acted on by a resultant force.
Zero resultant force means translational equilibrium: at rest or constant velocity.

Second law

Second law the resultant force is proportional to acceleration, F = ma, in the direction of the force.
Equivalent form — resultant force equals rate of change of momentum, F = Δp/Δt, valid for changing mass.
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)
A force opposing motion causes deceleration, not reversal of motion.

Third law

Third law if A exerts a force on B, B exerts an equal and opposite force on A.
A third-law pair must be the same type of force, equal in magnitude, opposite in direction and on different objects.
Book on tablethe weight and the normal force are not a pair — the pair of weight is the book's gravitational pull on Earth.

Part 3 of 8Contact and non-contact forces

Contact and non-contact forces

Contact forces act between touching objects

Contact forces act between touching objects friction, fluid resistance (drag), tension and the normal force.

Non-contact forces act at a distance through a field.

Gravitational force, with weight F_g = mg on Earth.
Electrostatic force, attractive or repulsive.
Magnetic force between poles or on moving charges.

Use the symbol given in the question

F_g is the syllabus symbol for weight, though W is often used.

Part 4 of 8Friction

1Friction opposes motion or prevents it

Friction opposes motion or prevents it and transfers energy by heating.

Surface friction acts parallel to the contact plane and depends on the normal force.

3Static friction matches the applied force up to a maximum

F_f ≤ μ_sF_N.

4Dynamic friction acts during sliding

F_f = μ_dF_N, a definite value.

5The maximum static friction is larger than dynamic friction

μ_s above μ_d, both between 0 and 1.

Fluid resistance (viscous drag) acts on bodies moving through a gas or liquid.

Part 5 of 8Hooke's law, Stokes' law and buoyancy

1Hooke's law

F = kΔx, for extension or compression of a spring or material up to its limit.
What the symbols mean: F = force (N) · k = spring constant (N m⁻¹) · x or e = extension (m)
k is the spring constant, the gradient of the straight part of a force–extension graph.
Use extension, not total length, and check which axis holds force.

2Stokes' law

Stokes' law viscous drag on a sphere F_d = 6πηrv.
η is the fluid viscosity, r the radius and v the speed.

3Buoyancy (upthrust)

F_b = ρVg, with ρ the fluid density and V the volume of fluid displaced.
A body floats when buoyancy equals its weight.

4Terminal speed of a sphere

Terminal speed of a sphere weight = drag + buoyancy, giving v = 2r²g(ρ_s − ρ_f) / 9η.
v is proportional to r² and inversely proportional to η.

Part 6 of 8Momentum, impulse and force

Momentum, impulse and force

Momentum p

Momentum p mv — a vector in kg m s^-1.

Conservation of linear momentum

Conservation of linear momentum total momentum before equals total momentum after, unless an external resultant force acts.
Take the direction of initial motion as positive; a rebound has negative velocity.

Impulse J

FΔt = Δp = mv − mu — in N s, in the direction of the force.

The equations apply for a constant force.
1 N = 1 kg m s^-2.

Increasing the time of impact reduces the force

Increasing the time of impact reduces the force a fielder's hands move back on catching a cricket ball.

Hail exerts more impulse on an umbrella than rain

Hail exerts more impulse on an umbrella than rain because it rebounds with a larger change in momentum.

Part 7 of 8Collisions and explosions

1Collision

Collision objects come together and exert forces for a short time;
- explosion — objects initially at rest are propelled apart.

2Momentum is always conserved

Momentum is always conserved kinetic energy may not be.

Type	Kinetic energy	Example
Elastic	Conserved	Particle collisions (ideal)
Inelastic	Not conserved	All macroscopic collisions
Totally inelastic	Maximum lost; bodies stick together	Moving as one mass
Explosion	Never conserved; starts at rest	Gun recoil, alpha emission

Collisions and explosions

Check the type

Check the type compare kinetic energy E_k = ½mv² before and after.

Kinetic energy is a scalar and never negative.

Two dimensions

Two dimensions conserve each component of momentum separately.
For an elastic collision with one body initially at rest, the final directions are 90° apart.

Part 8 of 8Circular motion

Circular motion

Uniform circular motion

Uniform circular motion constant speed with changing velocity, so there is acceleration.

Period T and frequency f

1/T — speed v = 2πr/T.

Angular displacement θ

Angular displacement θ s/r in radians — 2π rad = 360°.

Angular speed ω

Δθ/Δt = 2π/T = 2πf, in rad s^-1 — linear speed v = ωr.

Centripetal acceleration a

Centripetal acceleration a v²/r = ω²r = 4π²r/T², towards the centre.

Centripetal force F

Centripetal force F mv²/r = mω²r — the resultant force towards the centre.

It is not a separate force — it is tension, friction, gravity, electrostatic or magnetic force.
It does no work because it is perpendicular to the velocity.

Car on a flat bend

Car on a flat bend friction provides the force, so v_max = √(μgr).

Banked track

Banked track horizontal components of normal force and friction provide the force.

Vertical circle

Vertical circle tension is maximum at the bottom (mv²/r + mg) and minimum at the top (mv²/r − mg).

Key terms

Term	Meaning
Resultant force	Vector sum of all forces acting on a body.
Impulse	Force multiplied by time, equal to change in momentum.
Momentum	Product of mass and velocity.
Elastic collision	Collision in which kinetic energy is conserved.
Centripetal force	Resultant force towards the centre keeping a body in circular motion.
Buoyancy	Upward force from displaced fluid, ρVg.
Viscous drag	Frictional force between an object and a fluid.

Avoid these mistakes

Treating weight and the normal force as a third-law pair — they act on the same object.

Calling centripetal force a separate force rather than the resultant of real forces.

Forgetting the sign change of velocity, momentum and impulse on rebound.

Using ρ of the object instead of the fluid density in the buoyancy force.

Using angles in degrees for angular speed — use radians.

Last updated: 18 October 2026