Rotational Motion – Stage 1 (Page 10)

Rolling Motion – No-Slipping Condition & Dynamics

Rolling motion is a combination of translation and rotation. Almost every competitive exam contains at least one rolling-motion problem.

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1. What is Rolling Motion?

A body is said to be in rolling motion when it simultaneously rotates about its axis and translates along a surface.

Examples:
• Rolling wheel
• Rolling disc on an incline
• Cylinder moving without slipping

2. Condition for Pure Rolling (No Slipping)

v = ωR

where
v = velocity of center of mass
ω = angular velocity
R = radius of rolling body

This condition ensures the point of contact is momentarily at rest.

3. Velocity of Different Points on Rolling Body

✔ Velocity of topmost point = 2v
✔ Velocity of center = v
✔ Velocity of contact point = 0

This concept is frequently tested in objective questions.

4. Kinetic Energy of Rolling Body

Total kinetic energy of a rolling body:

K = ½ M v² + ½ I ω²

Both translational and rotational energies must be included.

5. Acceleration of Rolling Body on Inclined Plane

a = g sinθ / (1 + I / MR²)

This formula shows that acceleration depends on moment of inertia.

Order of acceleration (fastest to slowest):
✔ Solid sphere
✔ Solid cylinder
✔ Hollow cylinder / ring

6. Role of Friction in Rolling

✔ Friction is necessary for rolling
✔ No slipping occurs due to static friction
✔ Friction may do no work in pure rolling

⚠ Common Student Mistakes

❌ Forgetting rotational KE ❌ Using v ≠ ωR ❌ Assuming friction always opposes motion

IIT-JEE Insight

IIT often tests rolling motion using energy conservation instead of force equations. Choosing the faster method is crucial.

Stage 1 COMPLETE ✅
Next: Stage 2 – Board Exam Questions (Short + Long)

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