Key Fact
Linear–rotational analogy
Translation ↔ Rotation: F ↔ τ, m ↔ I, v ↔ ω, a ↔ α, p = mv ↔ L = Iω, KE = ½mv² ↔ KE_rot = ½ I ω². Newton's 2nd Law analogue: τ = I α.
-- NCERT Class 11 Physics, Ch. 6, p. 119Linear vs Rotational Comparison
8 MCQs12 revision cards9-step worked example
Source: NCERT System of Particles and Rotational MotionOfficial key: NTA-verifiedLast updated: 26 Sep 2026
Linear vs Rotational Comparison, explained for NEET
Every linear-motion quantity has a rotational twin. NCERT Class 11 Physics Chapter 6 (System of Particles and Rotational Motion), page 119, presents the comparison table that maps displacement → angular displacement, velocity → angular velocity, acceleration → angular acceleration, mass → moment of inertia, force → torque, momentum → angular momentum, and kinetic energy → rotational kinetic energy. This mapping is what NEET tests when it asks you to "write the rotational analogue of" a linear equation.
The structural rule is: replace every linear variable with its angular counterpart, and the equation's form stays identical.
| Linear | Symbol | Rotational | Symbol |
|---|---|---|---|
| Displacement | s | Angular displacement | θ |
| Velocity | v | Angular velocity | ω |
| Acceleration | a | Angular acceleration | α |
| Mass (inertia) | m | Moment of inertia | I |
| Force | F | Torque | τ |
| Momentum | p = mv | Angular momentum | L = Iω |
| Kinetic energy | ½mv² | Rotational KE | ½Iω² |
| Newton's 2nd law | F = ma | Rotational form | τ = Iα |
Two points where students lose marks:
1. The analogue of mass is I, not m. Moment of inertia depends on both mass AND its distribution about the axis. Two objects of the same mass can have different I values. When a question says "write the rotational analogue of ½mv²," the answer is ½Iω² — substituting m with I and v with ω.
2. Units shift but dimensional structure is preserved. Torque is N·m (not just N), angular momentum is kg·m²/s (not kg·m/s). If you write the rotational analogue but keep linear units, NEET marks it wrong.
The comparison table is a recall item — NEET can and does test it as a straightforward "which quantity is the analogue of..." question.
Can you answer these Linear vs Rotational Comparison MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Easy RecallPractice
The rotational analogue of linear momentum (p = mv) is:
Show answer and why every option is right or wrong
Answer: B. Linear momentum p = mv maps to angular momentum L = Iω, where mass m is replaced by moment of inertia I and velocity v by angular velocity ω (NCERT Class 11 Physics Chapter 6, page 119).
Why A is wrong: A is wrong because τ = Iα is the rotational analogue of Newton's second law F = ma, not of momentum.
Why C is wrong: C is wrong because ½Iω² is the rotational analogue of kinetic energy ½mv², not of momentum.
Why D is wrong: D is wrong because F = ma is a linear equation — it is not a rotational analogue of anything.
MCQ 2Easy RecallPractice
Which of the following is the rotational analogue of force?
Show answer and why every option is right or wrong
Answer: A. Force in linear motion corresponds to torque (τ = r × F) in rotational motion. Both cause a change in the state of motion in their respective domains (NCERT Class 11 Physics Chapter 6, page 119).
Why B is wrong: B is wrong because moment of inertia is the rotational analogue of mass, not of force.
Why C is wrong: C is wrong because angular momentum is the rotational analogue of linear momentum, not of force.
Why D is wrong: D is wrong because angular acceleration is the rotational analogue of linear acceleration, not of force.
MCQ 3Easy RecallPractice
In the rotational analogue of Newton's second law, mass (m) is replaced by:
Show answer and why every option is right or wrong
Answer: A. Newton's second law F = ma becomes τ = Iα in rotation. The quantity that replaces mass m (resistance to change in linear motion) is moment of inertia I (resistance to change in rotational motion). NCERT Class 11 Physics Chapter 6, page 119.
Why B is wrong: B is wrong because torque τ replaces force F, not mass.
Why C is wrong: C is wrong because angular momentum L replaces linear momentum p, not mass.
Why D is wrong: D is wrong because angular velocity ω replaces linear velocity v, not mass.
MCQ 4Direct ApplicationPractice
The rotational kinetic energy of a body rotating about a fixed axis is given by ½Iω². This expression is the rotational analogue of:
Show answer and why every option is right or wrong
Answer: D. ½Iω² is obtained by replacing m → I and v → ω in the linear kinetic energy expression ½mv². The structural form is identical (NCERT Class 11 Physics Chapter 6, page 119).
Why A is wrong: A is wrong because the rotational analogue of F = ma is τ = Iα, not ½Iω².
Why B is wrong: B is wrong because the rotational analogue of p = mv is L = Iω, not ½Iω².
Why C is wrong: C is wrong because the rotational analogue of work W = F·s is W = τ·θ, not ½Iω².
MCQ 5Direct ApplicationPractice
A disc of moment of inertia 4.0 kg·m² rotates at angular velocity 3.0 rad/s about a fixed axis. Its rotational kinetic energy is:
Show answer and why every option is right or wrong
Answer: D. KE_rot = ½Iω² = ½ × 4.0 × (3.0)² = ½ × 4.0 × 9.0 = 18.0 J. Direct substitution into the rotational KE formula (NCERT Class 11 Physics Chapter 6, page 119).
Why A is wrong: A is wrong — this results from computing ½ × I × ω = ½ × 4.0 × 3.0 = 6.0, forgetting to square ω.
Why B is wrong: B is wrong — 12.0 J comes from I × ω = 4.0 × 3.0, leaving out both the ½ and the square on ω.
Why C is wrong: C is wrong — this results from computing I × ω² = 4.0 × 9.0 = 36.0, forgetting the ½ factor.
MCQ 6Easy RecallPractice
In rotational motion, the quantity that plays the role that mass plays in linear motion is:
Show answer and why every option is right or wrong
Answer: B. B is correct. Mass measures a body's resistance to a change in its linear motion (F = ma). Moment of inertia measures resistance to a change in rotational motion (τ = Iα), and it appears in the same places: p = mv becomes L = Iω, and ½mv² becomes ½Iω².
Why A is wrong: A is wrong because torque is the rotational analogue of FORCE, the cause of angular acceleration, not the resistance to it.
Why C is wrong: C is wrong because angular momentum is the analogue of linear momentum, L = Iω corresponding to p = mv.
Why D is wrong: D is wrong because angular velocity is the analogue of linear velocity, the rate of change of angular position.
MCQ 7Concept TrapPractice
Two bodies A and B have the same mass and the same angular velocity about a fixed axis. If A has a larger moment of inertia than B, which statement is correct?
Show answer and why every option is right or wrong
Answer: C. KE_rot = ½Iω². Since ω is the same for both and I_A > I_B, body A has greater rotational KE. This illustrates that in rotation, inertia (I) replaces mass — and I depends on mass distribution, not just total mass (NCERT Class 11 Physics Chapter 6, page 119).
Why A is wrong: A is wrong because a larger I at the same ω gives a larger ½Iω², not smaller.
Why B is wrong: B is wrong because even though masses are equal, their moments of inertia differ. Rotational KE depends on I, not just m.
Why D is wrong: D is wrong because rotational KE depends on moment of inertia I (which accounts for mass distribution), not just on mass alone. Two bodies of the same mass can have different I values.
MCQ 8Easy RecallPractice
The linear equation v = u + at has the rotational analogue ω = ω₀ + αt. In this analogy, the quantity that replaces linear acceleration 'a' is:
Show answer and why every option is right or wrong
Answer: C. Comparing v = u + at with ω = ω₀ + αt term by term: v ↔ ω, u ↔ ω₀, a ↔ α, t ↔ t. Linear acceleration a is replaced by angular acceleration α (NCERT Class 11 Physics Chapter 6, page 119).
Why A is wrong: A is wrong because angular velocity ω replaces linear velocity v, not acceleration a.
Why B is wrong: B is wrong because torque τ replaces force F (in τ = Iα ↔ F = ma), not acceleration directly.
Why D is wrong: D is wrong because moment of inertia I replaces mass m, not acceleration.
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Linear vs Rotational Comparison: quick recall before you leave
How do you solve a Linear vs Rotational Comparison question? A worked example
- 1
Given
A uniform solid cylinder of mass M = 2.0 kg and radius R = 0.10 m rolls without slipping on a horizontal surface. Its centre of mass moves at v = 4.0 m/s.
- 2
Required
Find the ratio of rotational kinetic energy to translational kinetic energy.
- 3
Concept
For a rolling body, KE_total = KE_trans + KE_rot = ½Mv² + ½Iω². The linear–rotational analogy gives us the rotational KE term by replacing m with I and v with ω. For rolling without slipping, v = Rω, so ω = v/R.
- 4
Formula
KE_trans = ½Mv²
KE_rot = ½Iω²
For a solid cylinder about its symmetry axis: I = ½MR²
Rolling constraint: ω = v/R - 5
Substitution
KE_rot = ½ × (½MR²) × (v/R)²
= ½ × ½MR² × v²/R²
= ¼Mv²
KE_trans = ½Mv² - 6
Calculation
Ratio = KE_rot / KE_trans = (¼Mv²) / (½Mv²) = (¼)/(½) = 1/2
Note on exact constants: The coefficients ½ (in KE formulas and in the cylinder's MOI formula ½MR²) are exact mathematical/geometric constants. They do not limit significant figures. The given values M = 2.0 kg, R = 0.10 m, v = 4.0 m/s each have 2 significant figures, but since M, R, and v all cancel in the ratio, the answer is an exact fraction. - 7
Final answer
KE_rot / KE_trans = 1/2 (or equivalently, rotational KE is one-half of translational KE for a rolling solid cylinder).
This means one-third of the total KE is rotational and two-thirds is translational. - 8
Common trap
A common error is using the wrong MOI coefficient — plugging in I = MR² (ring) instead of I = ½MR² (solid cylinder). With the ring formula, the ratio would come out as 1 instead of ½. Always verify the geometry before picking I.
- 9
Similar NEET-style question
A solid sphere of mass 3.0 kg rolls without slipping at 5.0 m/s. What fraction of its total kinetic energy is rotational? (Hint: I_sphere = 2MR²/5; use the same ratio method.)
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What to remember before solving Linear vs Rotational Comparison questions
Which Linear vs Rotational Comparison formulas do you need for NEET?
1 formula — click to collapse
Rotational kinetic energy
Energy of rotation about an axis. Adds to translational KE for rolling bodies.
| Symbol | Quantity | SI Unit |
|---|---|---|
| I | moment of inertia | kg*m^2 |
| omega | angular velocity | rad/s |
Valid when
- Rotation about fixed axis
- I and omega about same axis
More in System of Particles and Rotational Motion: 7 exam traps and mistakes · 7 formulas · 4 question patterns from its other lessons.
Linear vs Rotational Comparison questions from past NEET papers
No question in our NEET 2020–2025 set targets this topic directly.
All 11 past-paper questions from System of Particles and Rotational Motion →
Sources
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
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