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Rotational Motion carries more JEE Main marks than almost any other mechanics chapter, and it is also the one students abandon first. It does not deserve that. The whole chapter is the linear mechanics you already know, with mass replaced by moment of inertia and force replaced by torque. Learn the standard moments of inertia cold and the rest is translation. Ten questions below. Give them ten honest minutes.
What this chapter carries in JEE Main
- Usually 2 to 3 questions every year, which is 8 to 12 marks.
- Moment of inertia and rolling down an incline are asked almost every year.
- Conservation of angular momentum fills the rest.
What the syllabus says
In the syllabus (Unit 5, Rotational Motion): Basic concepts of rotational motion, moment of a force, torque, angular momentum, conservation of angular momentum and its applications, moment of inertia, radius of gyration, moments of inertia of simple geometrical objects, the parallel and perpendicular axes theorems, equilibrium of rigid bodies, rigid body rotation and the equations of rotational motion, comparison of linear and rotational motion.
Taken from the NTA syllabus for JEE Main 2027. See the full syllabus, unit by unit.
Formulas you must know by heart
| Ring and disc | MR2 and MR2/2 |
| Solid and hollow sphere | 2MR2/5 and 2MR2/3 |
| Rod about its centre and its end | ML2/12 and ML2/3 |
| Parallel axis theorem | I = Icm + Md2 |
| Perpendicular axis theorem | Iz = Ix + Iy |
| Radius of gyration | k = √(I/M) |
| Torque and angular momentum | τ = Iα, L = Iω |
| Kinetic energy of a rolling body | KE = ½mv2(1 + k2/R2) |
| Rolling down an incline | a = g sinθ / (1 + k2/R2) |
| Conservation of angular momentum | I1ω1 = I2ω2 |
Everything about rolling comes out of the single factor k2/R2. It is 1 for a ring, ½ for a disc and 2/5 for a solid sphere, and the body with the smallest value always wins the race down the slope, whatever its mass or size.
Ten questions. Give yourself ten minutes.
Write your answers down before you scroll. A question you looked up is a question you have not answered.
Q1. The moment of inertia of a solid sphere about a diameter is
- (a) MR2
- (b) 2MR2/5
- (c) MR2/2
- (d) 2MR2/3
Q2. The moment of inertia of a uniform rod about an axis through one end and perpendicular to it is
- (a) ML2/12
- (b) ML2/3
- (c) ML2
- (d) ML2/2
Q3. A solid cylinder rolls without slipping down an incline of angle θ. Its acceleration is
- (a) g sinθ
- (b) 2g sinθ/3
- (c) 5g sinθ/7
- (d) g sinθ/2
Q4. A ring, a hollow sphere, a solid cylinder and a solid sphere are released together from the top of an incline. The one that reaches the bottom first is the
- (a) ring
- (b) hollow sphere
- (c) solid cylinder
- (d) solid sphere
Q5. A disc of moment of inertia I rotates at angular speed ω. An identical disc at rest is gently placed on it so that they turn together. The new angular speed is
- (a) ω
- (b) ω/2
- (c) 2ω
- (d) ω/4
Q6. The rotational equivalent of F = ma is
- (a) τ = Iω
- (b) τ = Iα
- (c) τ = I/α
- (d) τ = mα
Q7. For a solid sphere rolling without slipping, the ratio of its translational to its rotational kinetic energy is
- (a) 1 : 1
- (b) 5 : 2
- (c) 2 : 5
- (d) 7 : 2
Q8. The angular momentum of a rigid body rotating about a fixed axis is
- (a) Iα
- (b) Iω
- (c) I/ω
- (d) mvr2
Q9. The angular momentum of a body stays constant when
- (a) the net force on it is zero
- (b) the net external torque on it is zero
- (c) the body is at rest
- (d) always, without exception
Q10. The radius of gyration of a disc about its central axis is
- (a) R
- (b) R/√2
- (c) R/2
- (d) 2R
Answer key, with a hint for each
| Q1 | (b) | 2MR2/5. The hollow sphere is 2MR2/3, which is the usual distractor. |
| Q2 | (b) | Use the parallel axis theorem on ML2/12 with d = L/2. |
| Q3 | (b) | k2/R2 = ½ for a cylinder, so a = g sinθ/(3/2). |
| Q4 | (d) | Smallest k2/R2 wins, and 2/5 is the smallest of the four. |
| Q5 | (b) | Angular momentum is conserved: Iω = 2Iω′. |
| Q6 | (b) | Torque plays the part of force and moment of inertia the part of mass. |
| Q7 | (b) | ½mv2 against ⅕mv2, which is 5 : 2. |
| Q8 | (b) | L = Iω, exactly matching p = mv. |
| Q9 | (b) | A force alone can change the momentum without changing the angular momentum, provided it acts through the axis. |
| Q10 | (b) | k = √(I/M) = √(R2/2). |
Now mark yourself honestly
JEE Main marks the way it marks. Use the same rule here:
- +4 for a right answer
- −1 for a wrong one
- 0 for a blank
So ten questions here are out of 40. In the real paper, 25 Physics questions are out of 100.
If you scored 32 or more, the basics of this chapter are secure. Move to harder questions, not more of these.
If you scored below 24, do not feel bad about it. You have just found out something useful before the exam did. Go back to the formula table above, learn it properly, and sit these ten again tomorrow.
And if you guessed a few and they landed, count those as wrong. A guess that works once will not work in January.
The full chapter, on a clock
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