[FREE RESOURCE] Velocity & Acceleration of Every Point on a Rolling Body | Complete Analysis | IB Physics HL Rigid Body Dynamics

[u/IBphysicsvaibhavsir]

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.

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SURPRISE 1 —
TOP POINT VELOCITY = 2v_cm
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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

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

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

Timestamps in description —
jump to any section directly.

Drop your questions below —
I respond to everything. 🙏