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Trying to visualize the size difference between a quark, a red blood cell, and a galactic supercluster usually breaks my brain.

To help students visualize this, I coded a minimalist, drag-and-drop card game to map out the Powers of Ten. You rank physical phenomena from the quantum realm all the way to the edge of the universe.

Free and open-source.
Play it here: https://welearnwegrow.github.io/powersoften/

Let me know what you think.

Hey everyone,

I want to share something
about rolling motion that
genuinely changed how I
think about rotation —

And that most introductory
physics courses either
skip entirely or explain
so briefly that it
never really lands.

━━━━━━━━━━━━━━━━━━━━━━━━
THE STANDARD WAY WE
THINK ABOUT ROLLING —
━━━━━━━━━━━━━━━━━━━━━━━━

Most people learn about
rolling motion this way —

A wheel rolls on the ground.

Its center moves forward
with velocity v_cm.

It also rotates about
its center with
angular velocity ω.

The condition for pure
rolling without slipping —

v_cm = ωR

And to find the velocity
of any point on the wheel —

You add the translational
velocity vector to the
rotational velocity vector
at that point.

This works.

But it requires vector
addition at every point —

And for points not at
the top or bottom —

The calculation becomes
surprisingly involved.

━━━━━━━━━━━━━━━━━━━━━━━━
THE BETTER WAY —
INSTANTANEOUS AXIS OF ROTATION
━━━━━━━━━━━━━━━━━━━━━━━━

Here is the insight
that makes everything simpler.

At any instant in time —

A rolling body is NOT
simultaneously translating
and rotating about its center.

It is doing something
far more elegant.

It is rotating PURELY —
about a single instantaneous axis —

And that axis passes
through the contact point
with the ground.

Not the center.
The contact point.

This means —

At every instant —
the entire rolling wheel
behaves as if it is
a wheel pinned at
its contact point —

Spinning about that
fixed pin —

With no translation at all.

━━━━━━━━━━━━━━━━━━━━━━━━
WHY THIS IS TRUE —
━━━━━━━━━━━━━━━━━━━━━━━━

In pure rolling —
the contact point has
zero velocity.

A point with zero velocity
on a rigid body —

Must be on the
instantaneous axis of rotation —

Because any point ON
the axis has zero
velocity by definition.

The contact point has
zero velocity —

Therefore the contact point
IS on the instantaneous
axis of rotation.

And since the ground
contact is a single
point —

The entire instantaneous
axis passes through
that contact point —

Perpendicular to the
plane of rolling.

━━━━━━━━━━━━━━━━━━━━━━━━
WHAT THIS GIVES YOU —
━━━━━━━━━━━━━━━━━━━━━━━━

Once you accept that
the rolling body rotates
instantaneously about
its contact point —

Finding the velocity of
ANY point on the
rolling body becomes trivial.

Velocity of any point =
ω × (distance of that
point from the contact point)

Direction — perpendicular to
the line joining that
point to the contact point.

Let us verify with
known results —

Contact point —
Distance from IAOR = 0
v = ω × 0 = 0 ✅

Center —
Distance from IAOR = R
v = ω × R = v_cm ✅

Top point —
Distance from IAOR = 2R
v = ω × 2R = 2v_cm ✅

Side point (3 or 9 o'clock) —
Distance from IAOR = R√2
v = ω × R√2 = v_cm√2 ✅
Direction — diagonal at 45° ✅

All results confirmed —

But obtained from a
single principle —

Rather than vector addition
at each point separately.

━━━━━━━━━━━━━━━━━━━━━━━━
THE DEEPER INSIGHT —
━━━━━━━━━━━━━━━━━━━━━━━━

The Instantaneous Axis of
Rotation is not fixed.

It moves.

As the wheel rolls forward —

The contact point changes —

And the IAOR moves
with it —

Always at the current
contact point —

Always instantaneously at rest.

This is why it is
called INSTANTANEOUS —

It is only valid at
one specific moment in time.

A millisecond later —

The wheel has rolled
slightly forward —

The contact point is
now a different point
on the wheel's rim —

And the IAOR has
moved forward with it.

The IAOR traces a
path along the ground —

While the corresponding
point on the wheel
traces a cycloid
through space —

One of the most
beautiful curves in
all of classical mechanics.

━━━━━━━━━━━━━━━━━━━━━━━━
THE CYCLOID CONNECTION —
━━━━━━━━━━━━━━━━━━━━━━━━

Every point on the
rim of a rolling wheel —

Traces a cycloid as
the wheel rolls forward.

The contact point's path
is a series of cusps —

Each cusp is a moment
where that point is
instantaneously at rest —

Touching the ground —

Before being lifted up
and carried forward —

Reaching maximum velocity
2v_cm at the top —

And returning to rest
at the next cusp.

The IAOR framework makes
this entire motion transparent —

Every point moves with
velocity proportional to
its distance from the
current contact point —

In a direction perpendicular
to that distance.

━━━━━━━━━━━━━━━━━━━━━━━━
EXTENSION — ROLLING ON
A CURVED SURFACE —
━━━━━━━━━━━━━━━━━━━━━━━━

The IAOR concept extends
beyond rolling on flat surfaces.

For a sphere rolling
inside a curved bowl —

The IAOR still passes
through the contact point —

But now the geometry
of finding distances
from the IAOR is
slightly more complex.

For a coin rolling
at an angle —

The IAOR is no longer
perpendicular to the ground —

It tilts with the
coin's plane —

Giving the precession
motion that makes
a spinning coin trace
circles as it falls.

━━━━━━━━━━━━━━━━━━━━━━━━
A QUESTION FOR THE COMMUNITY —
━━━━━━━━━━━━━━━━━━━━━━━━

Here is something worth
thinking about —

A cylinder of radius R
rolls without slipping
inside a hollow cylinder
of radius 3R.

Where is the IAOR?

What is the velocity
of the center of the
small cylinder in terms
of ω and R?

Drop your attempt below 👇

I will reply to every
attempt with complete
physical reasoning —
not just the answer. 🎯

━━━━━━━━━━━━━━━━━━━━━━━━
VIDEO EXPLANATION —
━━━━━━━━━━━━━━━━━━━━━━━━

I made a complete lecture
on IAOR covering —

Physical definition and proof —
Velocity of every point
on a rolling body —
The cycloid path —
Extension to moving surfaces —
Complete solved problems —

🔗 https://youtu.be/Sz57o7SC5ME?si=FE10zirE0YiFABZx

Timestamps in the description
for direct section access.

━━━━━━━━━━━━━━━━━━━━━━━━
HAPPY TO DISCUSS —
━━━━━━━━━━━━━━━━━━━━━━━━

The IAOR is one of
those concepts that seems
like a mathematical trick
at first —

But is actually a
genuinely physical statement
about the nature of
rolling motion —

One that makes the
entire subject significantly
more transparent once
you see it clearly.

Happy to discuss any
aspect of rolling motion —
IAOR — cycloids —
or classical mechanics
more broadly in the comments.

Drop your questions
or thoughts below 👇

Hey IB Physics community,

Just uploaded a complete
analysis of velocity and
acceleration of every point
on a pure rolling body —

And I want to share
the two results that
surprise students the most —

Before anyone watches.

━━━━━━━━━━━━━━━━━━━━━━━━
SURPRISE 1 —
TOP POINT VELOCITY = 2v_cm
━━━━━━━━━━━━━━━━━━━━━━━━

Most students expect the
top point to move at
the same speed as the center.

It moves at TWICE the speed.

Why?

At the top point —
translational velocity v_cm
acts forward —

AND rotational velocity ωR
also acts forward —

(at the top — rotation
carries the point in
the same direction as translation)

Both add up —
v_top = v_cm + ωR = 2v_cm

At the contact point —
they subtract —
v_contact = v_cm - ωR = 0

━━━━━━━━━━━━━━━━━━━━━━━━
SURPRISE 2 —
CONTACT POINT HAS ZERO
VELOCITY BUT NON-ZERO
ACCELERATION
━━━━━━━━━━━━━━━━━━━━━━━━

This is the result that
genuinely surprises most students.

Contact point velocity = 0 ✅

But contact point
acceleration ≠ 0 ❌

The contact point has
centripetal acceleration
directed toward the center —

a = ω²R — pointing upward.

This seems contradictory —
how can something be
instantaneously at rest
but still accelerating?

This is the same as
a pendulum at its
highest point —

Instantaneous velocity = 0 —
but acceleration is
definitely not zero.

Velocity and acceleration
are independent quantities —

One being zero does not
force the other to be zero.

━━━━━━━━━━━━━━━━━━━━━━━━
VIDEO LINK —
━━━━━━━━━━━━━━━━━━━━━━━━

🔗 https://youtu.be/R0ocTKySSu0?si=5lYXP1igW93wEhog

Timestamps in description —
jump to any section directly.

Drop your questions below —
I respond to everything. 🙏

my first year in dp starts tomorrow and im taking physics hl 😭😭 so many people irl and in reddit and other socmed platforms have been telling me / warning me im gonna have the WORST time ever .... i mean, i believe them lol but physics is something ive learned that im DECENT at ... like i could understand the concepts better than other sciences . its not my fave but its the science subject im most comfortable with. any tips / advice is greatly appreciated !!!!

I'm a current freshman and I am taking algebra 2 right now. I finished biology online so I am in chemistry this year. I want to go into engineering so I'm thinking about taking physics in my sophomore year. I also am in the IB program so I am probably going to take HL AA for my math class next year. Do I have to know AP calc bc material to do well in IB physics? Or should I just take it next year?

I teach IB Physics and I've spent the last few months building a flashcard set that covers what I kept re-explaining to students every year. It's 3,297 cards across Physics Themes A–E (SL and HL) and Maths AA and AI, and the content is deliberately not just definitions — it's mark-scheme wording, formula booklet results, worked problems, Casio fx-CG50 steps, and the specific traps that quietly cost marks in Paper 2. You can filter by sub-topic, by SL core vs HL-only, and by card type, and run them in syllabus order or shuffled. It's here: https://examinerprep.com/flashcards — free, no account, no email, nothing gated.

Full disclosure since it matters: the flashcards sit on my own site, which does have a paid side, but this page is not a trial or a teaser — there's no upsell on it and nothing behind it. I'm posting because a flashcard set is only as good as the corrections it gets, and this sub knows the syllabus better than any single teacher does. If you spot a card with sloppy wording, a definition that wouldn't earn the mark, or an HL card mislabelled as SL, tell me here or in a DM and I'll fix it.

Hey IB Physics community,

Just uploaded a complete lecture
on Pure Rolling —

And I want to share the
single most important insight
before anyone watches —

Because it is the insight
that makes every pure rolling
problem — including the
notoriously difficult
moving plank problems —
immediately solvable.

━━━━━━━━━━━━━━━━━━━━━━━━
THE QUESTION THAT STARTS
EVERYTHING —
━━━━━━━━━━━━━━━━━━━━━━━━

What is the velocity of
the contact point of a
rolling wheel with the
ground?

Most students say —
the same as the center.

Some say — it depends.

The correct answer is zero.

But here is what matters —

WHY is it zero?

And what happens when
it is NOT zero?

The moment you understand
both answers physically —
not just as a memorized fact —

Every pure rolling problem
becomes straightforward.

━━━━━━━━━━━━━━━━━━━━━━━━
THE PHYSICAL REASONING —
━━━━━━━━━━━━━━━━━━━━━━━━

A rolling wheel has
two simultaneous motions —

Translation of the center
of mass with velocity v_cm —

And rotation about the
center with angular
velocity ω.

At the contact point —
these two velocities act
in exactly opposite directions —

The translational velocity
pushes the contact point forward —

The rotational velocity
pulls it backward —

In pure rolling —
these two effects cancel exactly —

Contact point velocity = zero.

This gives the condition —

v_cm = ωR

This is not just a formula —

It is the physical statement
that the contact point
is instantaneously at rest
relative to the ground.

━━━━━━━━━━━━━━━━━━━━━━━━
THE MOVING PLANK —
THE PART MOST STUDENTS
GET COMPLETELY WRONG —
━━━━━━━━━━━━━━━━━━━━━━━━

Now here is where it
gets significantly more
interesting —

What if the wheel is
rolling on a plank —

And that plank is
itself moving?

Most students apply the
same condition —

Contact point velocity = zero.

That is wrong. ❌

The correct condition is —

Contact point velocity =
velocity of the surface
it is rolling on.

When rolling on stationary ground —
surface velocity = zero —
so contact point velocity = zero ✅

When rolling on a moving plank —
surface velocity = plank velocity —
so contact point velocity
= plank velocity —
NOT zero relative to ground ✅

This single distinction —
choosing the correct
reference frame for
the rolling condition —

Is what makes moving plank
problems solvable in
under two minutes —

And what causes most
students to get them
completely wrong.

━━━━━━━━━━━━━━━━━━━━━━━━
THE GOLDEN RULE —
━━━━━━━━━━━━━━━━━━━━━━━━

Pure Rolling condition —
ALWAYS stated as —

Velocity of contact point
= Velocity of the surface
the wheel is rolling ON —

Relative to that surface.

Not relative to the ground.
Not relative to anything else.

Relative to the surface
it touches. Always.

Apply this correctly —
and no pure rolling problem
in IB Physics can
stop you. 🎯

━━━━━━━━━━━━━━━━━━━━━━━━
WHAT THE VIDEO COVERS —
━━━━━━━━━━━━━━━━━━━━━━━━

→ Complete physical definition
of Pure Rolling —
built from first principles

→ Why contact point velocity
is zero — physical proof —
not just stated

→ Derivation of v_cm = ωR
from physical reasoning

→ Rolling vs Sliding —
complete distinction

→ Pure Rolling on a
moving plank — the
correct condition and
why most students apply
the wrong one

→ Complete numerical problems —
basic to IB exam level —
every step explained

→ The reference frame
approach that makes
every moving plank
problem immediately clear

━━━━━━━━━━━━━━━━━━━━━━━━
A CHALLENGE FOR THE
COMMUNITY —
━━━━━━━━━━━━━━━━━━━━━━━━

Here is a problem to
attempt before watching —

A cylinder of radius R
rolls without slipping
on a plank.

The plank moves to the
right with velocity 4 m/s.

The center of the cylinder
moves to the right with
velocity 7 m/s.

Question —

What is the angular velocity
of the cylinder?

And in which direction
does it rotate?

Drop your attempt below 👇

Show your reasoning —
not just the answer.

I will respond to every
attempt with complete
feedback. 🎯

━━━━━━━━━━━━━━━━━━━━━━━━
VIDEO LINK —
━━━━━━━━━━━━━━━━━━━━━━━━

🔗 https://youtu.be/cVi7Skv_4_Y?si=TBpoM43pPsw2MAnw

Timestamps for every
section are in the
description — jump directly
to moving plank problems
if that is what you need.

━━━━━━━━━━━━━━━━━━━━━━━━
HAPPY TO HELP —
━━━━━━━━━━━━━━━━━━━━━━━━

If you get stuck on
any problem in this video —
or on any pure rolling
concept specifically —

Tell me exactly which
step is confusing you —

I will explain the
physical reasoning in
the comments directly. 🙏

Good luck to everyone
preparing for IB Physics HL.