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.2.18 Centripetal Acceleration — IB Physics HL Revision Notes & Topical Questions

5 min read 10 parts Lesson 29 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.2.18 Centripetal Acceleration — IB PHYSICS SL notes: Define centripetal acceleration, derive a = v²/r = ω²r and explain that its direction is towards the centre.Centripetal acceleration = the acceleration of an object towards the centre of a circle when it moves around the circ…

In terms of speed
In terms of angular speed
In terms of period
Data booklet
Linear speed
What the symbols mean

Part 1 of 8Why there is an acceleration

Centripetal acceleration

Centripetal acceleration the acceleration of an object towards the centre of a circle when it moves around the circle at constant speed.

Reason

Reason velocity is a vector, so a changing direction at constant speed is a changing velocity.

Direction

Direction it is directed towards the centre and is perpendicular to the velocity.
It is in the same direction as the centripetal force.

Effect

Effect it changes only the direction of the velocity, not its size.

Part 2 of 8The equations

The equations

In terms of speed

In terms of speed a = v²/r, where v is the linear speed and r the radius.

In terms of angular speed

In terms of angular speed a = ω²r, using v = ωr.
What the symbols mean: a = centripetal acceleration towards the centre (m s⁻²) · v = speed (m s⁻¹) · ω = angular speed (rad s⁻¹) · r = radius (m)

In terms of period

In terms of period a = 4π²r/T², using ω = 2π/T = 2πf.

Unit

Unit m s⁻².

Data booklet

Data booklet it gives the equations in several forms; choose the one that matches the data (v or ω).

Part 3 of 8Derivation

The object moves through a small angle Δθ in a short time Δt on a circle of radius r.

The initial and final velocity vectors both have magnitude v and the angle between them is Δθ.

The change in velocity forms the base of an isosceles triangle, so Δv ≈ vΔθ for small Δθ.

Dividing by Δt gives a = Δv/Δt = vω.

Using ω = v/r gives a = v²/r = ω²r.

Direction
- for small Δθ the vector Δv is perpendicular to the velocity and points towards the centre.

Part 4 of 8Relations in uniform circular motion

1Linear speed

Linear speed v = ωr = 2πr/T.
What the symbols mean: v = speed (m s⁻¹) · ω = angular speed (rad s⁻¹) · r = radius (m) · T = period (s)

2Angular speed

ω = 2π/T = 2πf.
What the symbols mean: ω = angular frequency (rad s⁻¹) · f = frequency (Hz) · T = period (s)

3Acceleration

Acceleration a = vω = v²/r = ω²r.

4Constant magnitude

Constant magnitude the acceleration vector rotates with the position and its size is constant.

5Average over a revolution

Average over a revolution it is zero, since the velocity returns to its initial value, though the instantaneous acceleration is never zero.

6Half a revolution

Half a revolution the change in velocity is 2v, so the average acceleration is 4v/T.

Part 5 of 8Using the formula

Proportions

Proportions a is proportional to v² at fixed radius and inversely proportional to r at fixed speed.

Same ω

Same ω a person farther from the centre of a turntable has the greater acceleration, since a = ω²r.

Force

F = ma gives the centripetal force mv²/r.

Centrifuge

Centrifuge a rim at radius 0.10 m and 3000 revolutions per minute has a ≈ 9.9 × 10³ m s⁻², about 1000 g.

Fairground ride

Fairground ride it may give 3 g to 4 g.

Moon

Moon with r = 3.84 × 10⁸ m and T = 27.3 days, a = 2.7 × 10⁻³ m s⁻², which supported the inverse-square law of gravity.

Part 6 of 8Visualising with a velocity circle

Hodograph

Hodograph velocity vectors drawn from one point have tips on a circle of radius v.

Tip speed

Tip speed the tip moves round at angular velocity ω, so its speed is vω, the size of the acceleration.

Direction

Direction the acceleration is tangent to the hodograph, perpendicular to the velocity and towards the centre.

Misconception avoided

Misconception avoided the acceleration does not point along the direction of motion.

Part 7 of 8Explaining in an answer

1Step 1

Step 1 the speed is constant but the direction of the velocity changes.

2Step 2

Step 2 the change in velocity points towards the centre.

3Step 3

Step 3 so the acceleration is towards the centre, perpendicular to the velocity, with size v²/r.

Part 8 of 8More from the specification

1Resultant centripetal force requirement

Resultant centripetal force requirement moving along circular paths requires a resultant centripetal force directed towards the centre, provided by friction or tension.

2Newtonian action and reaction forces

Newtonian action and reaction forces according to Newton's third law, circular centripetal forces are accompanied by equal and opposite reactionary contact forces.

3Centripetal acceleration in fluid vortices

Centripetal acceleration in fluid vortices particles circling in rotating fluid streams experience radial centripetal acceleration acting perpendicular to instantaneous tangential velocity.

4Centripetal acceleration formula

An object in uniform circular motion at constant speed v and radius r undergoes inward radial acceleration: a_c = v² / r = omega² * r.

5Centripetal force requirements

Maintaining a curved trajectory requires a resultant inward force (F_c = m * v² / r), provided by tension, friction,
or gravitational attraction.

6Banked curves and friction

On banked roadway curves, the horizontal component of the normal contact force provides centripetal acceleration,
reducing reliance on tire friction.

7Fluid resistance

Drag force from a fluid opposing motion.

8Normal

Line at 90° to a surface.

9Tension

Force transmitted along a string or rope.

10Buoyancy

Another name for upthrust.

11Static friction

Friction between surfaces at rest relative to each other; f_s ≤ μ_sF_N.

12Circular motion

Motion along a circular path with a force towards the centre.

13Kinetic energy

K = ½mv², energy of motion.

14Normal reaction

The contact force perpendicular to a surface.

15Reaction force

Force from a support pushing up on an object.

16Momentum

P = mv, a vector.

17Resultant

Vector sum of two or more vectors.

18Friction

Force parallel to the surface opposing relative motion or its tendency.

19Newton

Unit of force, kg m s^-2.

20Weight

Gravitational force on a mass.

21Collision

Short interaction with large internal forces.

22Impulse

J = FΔt = Δp.
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)

Key terms

Term	Meaning
Centripetal acceleration	Acceleration towards the centre of a circle for a body moving in a circle at constant speed
Linear (tangential) speed	Speed along the circular path
Angular speed	Rate of change of angular displacement, in rad s⁻¹
Period	Time for one complete revolution
Uniform circular motion	Motion in a circle at constant speed
Hodograph	Plot of velocity vectors drawn from a common point

Avoid these mistakes

Saying there is no acceleration because the speed is constant — the velocity direction changes.

Pointing the acceleration along the direction of motion — it points to the centre.

Using the diameter for r — use the radius.

Using degrees for ω — use rad s⁻¹.

Thinking the acceleration changes the speed — it changes only the direction.

Last updated: 15 October 2026