Skip to content
Dabour HubLEARN · PRACTICE · EXPLORESign inStudent

Theme A — Space, Time and Motion

A.4.5 Moment of Inertia — IB Physics HL Revision Notes & Topical Questions

5 min read 8 parts Lesson 47 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision
🩺
100% Curriculum Specification Match Lesson Doctor Verified
The only platform with 100% curriculum specification match and verified interactive question banks.
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.
0%read
Lesson summary

A.4.5 Moment of Inertia — IB PHYSICS HL notes: Define moment of inertia and calculate it for point masses and combined systems.Inertia = the resistance to a change of linear motion — a larger mass has greater inertia.Moment of inertia = the resistance to a change of rotational mo…

  • Mass distribution
  • System of point masses
  • You need not memorise them
  • Axis of rotation
  • Rigid body
  • Total moment of inertia

Part 1 of 6Inertia and moment of inertia

Inertia
Inertia the resistance to a change of linear motion — a larger mass has greater inertia.
Moment of inertia
Moment of inertia the resistance to a change of rotational motion — depending on the distribution of mass about the chosen axis.
Unit
  • Unit kg m2.
It shows how easy or hard it is to rotate a body.

Part 2 of 6Factors affecting I

Shape of the body.
Density of the body.
Orientation relative to the axis of rotation.
Mass distribution
  • Mass distribution mass farther from the axis increases I.
The same object has different I for different axes.
  • A thin rod about its centre, about one end, or about its vertical axis each gives a different value.
There is an infinite number of possible axes and so of moments of inertia.

Part 3 of 6Point masses and systems

Point masses and systems
Point mass
  • I = mr2, with r the distance from the axis.
System of point masses
  • Itot = Σmr2.
The total moment of inertia of a composite body is the sum of the moments of its parts.
  • A dumbbell with two spheres and a rod has Itot = 2Isphere + Irod.
  • For spheres of I = 0.04 kg m2 each and a rod of 1.62 × 10-3 kg m2, Itot = 0.0816 kg m2, with the rod contributing about 2%.

Part 4 of 6Moments of inertia of shapes

Moments of inertia of shapes
The moments of inertia of common shapes (rods, discs, cylinders, spheres) are given in exam questions.
Examples used in the course.
  • Solid sphere about a diameter(2/5)mr2.
  • Cylinder or disc about its axis½mr2.
You need not memorise them
  • You need not memorise them but you must know how to use them and add them.

Part 5 of 6Linear and rotational analogy

LinearRotational
Mass mMoment of inertia I
Force FTorque τ
Velocity vAngular velocity ω
Momentum p = mvAngular momentum L = Iω
Linear and rotational analogy
Take care to distinguish linear from rotational motion when masses are spread around an axis.
Moment of inertia plays the role of mass in rotation.

Part 6 of 6More from the specification

More from the specification
Moment of Inertia (I) Defined
  • The moment of inertia of a rigid body about a specified axis is the rotational analogue of mass, defined as I = Σ mi ri² (kg m²), measuring resistance to angular acceleration.
Torque and Rotational Dynamics
  • The rotational form of Newton's second law states that resultant external torque τ produces an angular acceleration α according to τ = Iα,
  • where torque is τ = Fr sin θ.
Rotational Equilibrium and Couples
  • A system is in rotational equilibrium when the sum of clockwise torques equals the sum of anticlockwise torques (Σ τ = 0);
    • a couple consists of two equal and opposite parallel forces producing pure torque.
Rotational Kinetic Energy
  • A rotating rigid body possesses rotational kinetic energy given by Ek = ½Iω², conserving total mechanical energy alongside translational kinetic and gravitational potential energy.
Impulse
  • 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)
Radius
  • Distance from the centre to the circular path.
Constant
  • Not changing.
Angular impulse
  • Product of net torque and the time it acts, τΔt.
Kinetic energy
  • K = ½mv2, energy of motion.
Acceleration
  • Rate of change of velocity.
Resultant
  • Vector sum of two or more vectors.
Displacement
  • Change in position.
Couple
  • A pair of equal opposite forces with different lines of action.
Clockwise
  • Turning in the direction of a clock's hands.
Equilibrium
  • State with zero net force.
Newton
  • Unit of force, kg m s-2.
Perpendicular
  • At right angles.

Key terms

TermMeaning
Moment of inertiaResistance to change in rotational motion, depending on mass distribution about an axis.
InertiaResistance to change in linear motion.
Axis of rotationLine about which a body rotates.
Point massMass concentrated at one point, I = mr2.
Rigid bodyBody whose shape does not change when rotating.
Total moment of inertiaSum of the moments of inertia of the parts.

Avoid these mistakes

1
Treating I as a fixed property of the object regardless of the axis.
2
Using the distance to the object's edge instead of to the axis.
3
Forgetting to square r in I = mr2.
4
Adding moments of inertia about different axes.
5
Memorising shape formulae when they will be given.

Last updated:

\n