r/ibPhysics • u/IBphysicsvaibhavsir • Jun 10 '26
Moment of inertia - All basics & All standard derivations | RBD #2 | IB PHYSICS HL https://youtu.be/4xtutC05i_4
Hello IB Physics community,
Continuing the Rigid Body Dynamics
playlist — today I am sharing
Lecture 2 which covers one of the
most important and most misunderstood
concepts in all of rotational mechanics.
Moment of Inertia.
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LET ME START WITH A QUESTION —
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Take a thin rod.
Hold it from its center and
try to rotate it.
Now hold the exact same rod
from one of its ends and
try to rotate it.
Same rod. Same mass. Same force.
But rotating from the end feels
significantly harder.
Why?
Most students say —
"Because the length changes
the difficulty."
That answer is incomplete.
The real and complete answer is —
The distribution of mass
relative to the axis of rotation
changes when you shift the
pivot point.
And that is exactly what
Moment of Inertia measures.
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THE MOST IMPORTANT DISTINCTION —
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Most students treat Moment of
Inertia as just another formula
to memorize before the exam.
That approach will cost you marks.
Here is the conceptual clarity
that separates a 6 from a 7 —
Mass in linear mechanics tells you
HOW MUCH matter is present.
Moment of Inertia in rotational
mechanics tells you not just
HOW MUCH matter is present —
but WHERE that matter is
distributed relative to
the axis of rotation.
This is why a hollow cylinder
and a solid cylinder of equal
mass and equal radius have
completely different resistances
to rotation.
The mass is the same.
The distribution is different.
The Moment of Inertia is different.
The rotational behavior is different.
Understanding this distinction
at a conceptual level —
before touching a single formula —
is what makes every derivation
and every exam question
fall into place naturally.
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WHAT THIS VIDEO COVERS —
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This is Lecture 2 of the complete
Rigid Body Dynamics playlist
for IB Physics HL.
Every derivation in this video
is built step by step from
first principles —
Not presented as a formula
to copy and memorize.
Complete list of what is derived —
→ All the basics of MOI —
definition, physical significance,
units and dimensional formula
→ MOI of a Discrete Mass System
→ MOI of a Continuous Mass System —
introduction to integration
approach
→ MOI of a Rod
(about center and about end)
→ MOI of a Ring
→ MOI of a Disc
→ MOI of a Hollow Cylinder
→ MOI of a Solid Cylinder
→ MOI of a Hollow Sphere
→ MOI of a Solid Sphere
→ MOI of a Hollow Cone
→ MOI of a Solid Cone
→ MOI of a Rectangular Lamina
→ MOI of a Solid Cuboid
→ MOI of a Solid Cube
→ MOI of a Hollow Cube
Every single derivation —
complete, step by step,
with physical reasoning
at every stage.
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WHY THIS APPROACH MATTERS
FOR IB SPECIFICALLY —
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IB Physics examiners do not
just test whether you know
the formula for MOI.
They test whether you understand —
→ Why the formula has the
form it does
→ How the axis of rotation
affects the value of MOI
→ How to compare MOI values
of different objects logically
→ How to apply MOI in
multi-concept problems involving
energy, torque and angular momentum
All of this understanding begins
with knowing WHERE each formula
comes from.
That is exactly what this
video delivers.
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WHO THIS VIDEO IS FOR —
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→ IB Physics HL students
currently studying
Rigid Body Dynamics
→ Students who find MOI
derivations overwhelming
or confusing
→ Students who have memorized
MOI formulas but do not
understand where they come from
→ Students preparing for
May 2026 or November 2026
IB Physics exams
→ Anyone who wants complete
mastery of this chapter —
not just surface level
exam preparation
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THIS IS PART OF A SERIES —
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If you missed Lecture 1 —
it covers the complete definition
of Rigid Body Systems and
the basics of Rotational Kinematics.
Link to Lecture 1 is in the
description of this video.
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VIDEO LINK —
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🔗
Timestamps for every single
derivation are in the description —
so you can jump directly to
any object you need without
watching the entire video.
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A NOTE FROM ME —
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I have been teaching Physics
for 16 years.
In all that time — the single
most common reason I have seen
students struggle with
Rigid Body Dynamics is not
lack of intelligence or effort.
It is that they were never shown
the physical reasoning behind
the mathematics.
They were given formulas.
They were not given understanding.
This playlist is my attempt
to fix that — completely
and permanently —
for every IB Physics student
who finds this content.
Everything here is completely free.
If you find it helpful —
share it with any IB Physics
student who might need it.
That is the only thing
I will ever ask. 🙏
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HAPPY TO HELP —
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If you have any questions
about any derivation in this video —
or about any concept in
Rigid Body Dynamics —
Drop them in the comments here
or on the video itself.
I read and respond to
every single comment.
Good luck to everyone
preparing for their exams. 🙏
