Physics · JEE Advanced only

Rolling Without Slipping (JEE Advanced)

Not in the JEE Main syllabus, but it is in JEE Advanced. Study time: about 6 to 8 hours. Spend 2 hours on the basic constraint and energy formulas, 2 hours on incline problems with different shapes, and 2 to 4 hours on mixed problems involving friction limits, acceleration, and combined rotation-translation scenarios..

Last updated: 26 October 2026

Direct answer

Rolling without slipping is when an object like a ring, cylinder, or sphere rolls on a surface such that the point of contact has zero velocity relative to the surface.

Rolling without slipping is when an object like a ring, cylinder, or sphere rolls on a surface such that the point of contact has zero velocity relative to the surface. This means the object is not skidding or sliding, and there is a fixed relationship between its linear and angular motion. It combines translational and rotational motion into one elegant constraint.

Official syllabus

What the JEE Advanced syllabus says

“Rolling without slipping of rings, cylinders and spheres”

Source: JEE Advanced 2026 Information Bulletin, Annexure-I. Closest JEE Main topic: rigid body rotation and equations of rotational motion.

JEE Main covers basic rotational motion, but Advanced specifically tests rolling on inclines, energy methods for rolling bodies, and friction analysis during rolling. You need to master the constraint equation and energy distribution that Main does not emphasize.

Key ideas

What you must understand

The no-slip condition means v = ωR, where v is the velocity of the center of mass and ω is the angular velocity
For rolling bodies, kinetic energy has two parts: translational (½mv²) and rotational (½Iω²)
Different shapes have different moments of inertia, so a ring, solid cylinder, and solid sphere roll down an incline at different speeds
Friction is necessary for rolling without slipping, but it does no work if there is no slipping
On an incline, the body with the smallest I/(mR²) ratio reaches the bottom fastest
When analyzing rolling problems, you can use either force/torque equations or energy conservation, depending on what is asked

Formulas

Formulas and key facts

v = ωR (no-slip condition)
KE_total = ½mv² + ½Iω² = ½mv²(1 + I/mR²)
a = gsinθ / (1 + I/mR²) for rolling down incline
I_ring = mR², I_solid cylinder = ½mR², I_solid sphere = (2/5)mR²
Friction f = (I/R) × α = (I/R²) × a for rolling
For pure rolling: v² = 2gh / (1 + I/mR²) after falling height h
Minimum friction coefficient for rolling without slipping on incline: μ ≥ tanθ / (1 + mR²/I)

Avoid

Common mistakes

Forgetting to include rotational kinetic energy when using energy conservation
Using v = ωR even when the problem says there is slipping (read carefully)
Confusing the direction of friction: for rolling down an incline, friction acts up the slope
Using the wrong moment of inertia formula for the given shape (ring vs cylinder vs sphere)

Worked example

A JEE Advanced-level example

Question. A solid sphere of mass 2 kg and radius 0.1 m starts from rest and rolls without slipping down an incline of height 1.4 m. Find its speed at the bottom of the incline. Take g = 10 m/s².

Show solution

Use energy conservation: mgh = ½mv² + ½Iω²
For solid sphere, I = (2/5)mR² and ω = v/R, so ½Iω² = ½ × (2/5)mR² × (v/R)² = (1/5)mv²
Total KE = ½mv² + (1/5)mv² = (7/10)mv²
Set mgh = (7/10)mv², so v² = 10gh/7
v² = 10 × 10 × 1.4 / 7 = 140/7 = 20
v = √20 = 2√5 m/s ≈ 4.47 m/s

Answer: v = 2√5 m/s (approximately 4.47 m/s)

Solved twice independently; both solutions agree.

FAQs

Frequently asked questions

Is Rolling Without Slipping in the JEE Main syllabus?

No. It is in the JEE Advanced 2026 syllabus only. The closest JEE Main topic is rigid body rotation and equations of rotational motion.

How long does Rolling Without Slipping take to prepare for JEE Advanced?

About 6 to 8 hours. Spend 2 hours on the basic constraint and energy formulas, 2 hours on incline problems with different shapes, and 2 to 4 hours on mixed problems involving friction limits, acceleration, and combined rotation-translation scenarios., if you already know the related JEE Main topic.