For uniform angular acceleration α: ω = ω₀ + α t; θ = ω₀ t + ½ α t²; ω² = ω₀² + 2 α θ. Rotational analogues of the linear kinematic equations.
-- NCERT Class 11 Physics, Ch. 6, p. 117Rotational Equations of Motion
8 MCQs3 revision cards9-step worked example
Source: NCERT System of Particles and Rotational MotionPYQ coverage: NEET 2022Official key: NTA-verifiedLast updated: 25 Sep 2026
Rotational Equations of Motion, explained for NEET
The trap that costs marks: a flywheel problem gives angular speed in rpm. You plug the number straight into ω = ω₀ + αt. The arithmetic looks clean. The answer matches one of the options — the wrong one. You just forgot to convert rpm to rad/s.
This is the single in-scope trap for rotational equations of motion, and it appears with reliable frequency in NEET papers.
What the equations are. When a rigid body rotates about a fixed axis with constant angular acceleration α, the motion obeys three kinematic equations that mirror the linear ones (NCERT Class 11 Physics, Chapter 6, page 105):
- ω = ω₀ + αt
- θ = ω₀t + ½αt²
- ω² = ω₀² + 2αθ
Here ω is angular velocity (rad/s), α is angular acceleration (rad/s²), θ is angular displacement (rad), and t is time (s). These hold only when α is constant and rotation is about a single axis.
The rotational kinetic energy of a body spinning at ω about a fixed axis is KE_rot = ½Iω² (NCERT Class 11 Physics, Chapter 6, page 106), where I is the moment of inertia about that axis.
The bridge to NEET. Flywheel and grinding-wheel problems are a staple. They give initial and final speeds (often in rpm), a time interval, and ask for angular acceleration or total revolutions. The physics is straightforward — the danger is entirely in units.
Watch-out: 1 rpm = 2π/60 rad/s. Convert before substituting. Also, if a question asks for "number of revolutions," remember that θ from the kinematic equation is in radians — divide by 2π to get revolutions.
Can you answer these Rotational Equations of Motion 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
What is the SI unit of angular acceleration?
Show answer and why every option is right or wrong
Answer: D. Angular acceleration is the rate of change of angular velocity. In SI, angular velocity is in rad/s, so angular acceleration is rad/s² (NCERT Class 11 Physics, Chapter 6, page 105).
Why A is wrong: A is wrong because rpm is not an SI unit; it must be converted to rad/s before use in kinematic equations.
Why B is wrong: B is wrong because revolutions are not SI units; one revolution equals 2π radians.
Why C is wrong: C is wrong because degrees are not the SI unit of angle; the SI unit of angle is the radian.
MCQ 2Easy RecallPractice
Which of the following is a necessary condition for using the equation ω = ω₀ + αt?
Show answer and why every option is right or wrong
Answer: B. The rotational kinematic equations are derived under the assumption of constant angular acceleration α, analogous to how v = u + at requires constant linear acceleration (NCERT Class 11 Physics, Chapter 6, page 105).
Why A is wrong: A is wrong because these equations apply to any rigid body rotating about a fixed axis, not just point particles.
Why C is wrong: C is wrong because ω₀ can take any value; the equation accommodates non-zero initial angular velocity.
Why D is wrong: D is wrong because the axis need not pass through the centre of mass — it only needs to be a fixed axis with constant α.
MCQ 3Direct ApplicationPractice
A wheel starts from rest and reaches an angular velocity of 6.0 rad/s in 3.0 s under constant angular acceleration. What is the angular acceleration?
Show answer and why every option is right or wrong
Answer: A. Using ω = ω₀ + αt with ω₀ = 0, α = ω/t = 6.0/3.0 = 2.0 rad/s² (NCERT Class 11 Physics, Chapter 6, page 105).
Why B is wrong: B is wrong because it inverts the ratio, α = t/ω = 3.0/6.0 = 0.50; the correct formula gives α = (ω − ω₀)/t = 6.0/3.0 = 2.0.
Why C is wrong: C is wrong because this is ω × t = 6.0 × 3.0 = 18 divided by 2 — a confusion with the displacement formula, not the acceleration formula.
Why D is wrong: D is wrong because 18 = ω × t, which is not how angular acceleration is calculated; α = Δω/Δt, not ω × t.
MCQ 4Direct ApplicationPractice
A grinding wheel spinning at 9.00 × 10² rpm is brought to rest in 3.0 s under constant angular deceleration. What is the magnitude of the angular deceleration?
Show answer and why every option is right or wrong
Answer: A. First convert: ω₀ = 900 × 2π/60 = 30π rad/s. Then α = (0 − 30π)/3.0 = −10π rad/s²; magnitude is 10π rad/s² ≈ 31.4 rad/s² (NCERT Class 11 Physics, Chapter 6, page 105).
Why B is wrong: B is wrong because rpm/s is not an SI unit; angular deceleration must be expressed in rad/s², requiring conversion of 900 rpm to 30π rad/s first.
Why C is wrong: C is wrong because it uses ω₀ = 900 rad/s without converting from rpm — this is the classic rpm-to-rad/s trap. 900 rpm ≠ 900 rad/s.
Why D is wrong: D is wrong because this value (150) arises from dividing 900 by 6 or some other incorrect shortcut that omits the 2π/60 conversion factor.
MCQ 5Direct ApplicationPractice
A fan blade accelerates uniformly from rest to 1.20 × 10³ rpm in 4.0 s. How many complete revolutions does it make in this time?
Show answer and why every option is right or wrong
Answer: D. Convert: ω = 1200 × 2π/60 = 40π rad/s. Using θ = ω₀t + ½αt² with ω₀ = 0: first find α = 40π/4.0 = 10π rad/s², then θ = ½ × 10π × 16 = 80π rad. Number of revolutions = 80π/(2π) = 40 (NCERT Class 11 Physics, Chapter 6, page 105).
Why A is wrong: A is wrong because 4800 = 1200 × 4 — multiplying rpm by time directly, ignoring both the factor-of-2 for uniform acceleration and the unit conversion.
Why B is wrong: B is wrong because it likely comes from computing θ in radians (80π) and dividing by π instead of 2π, giving 80 instead of 40.
Why C is wrong: C is wrong because 2400 = 1200 × 4/2 — treating rpm as if it were already in revolutions per second and averaging, without any conversion to radians.
MCQ 6CalculationPractice
A flywheel rotating at 6.00 × 10² rpm decelerates uniformly at 2π rad/s² until it stops. What is the total angular displacement in radians?
Show answer and why every option is right or wrong
Answer: C. Step 1 — convert: ω₀ = 600 × 2π/60 = 20π rad/s. Step 2 — use ω² = ω₀² + 2αθ with ω = 0 and α = −2π: 0 = (20π)² + 2(−2π)θ → 4π²(100) = 4πθ → θ = 100π rad (NCERT Class 11 Physics, Chapter 6, page 105).
Why A is wrong: A is wrong because 100π² comes from dropping the π from α: dividing (20π)² by 2 × 2 = 4 instead of by 2 × 2π = 4π.
Why B is wrong: B is wrong because 200π comes from θ = ω₀²/α, dropping the 2 in ω² = ω₀² + 2αθ: (20π)²/(2π) = 200π.
Why D is wrong: D is wrong because 1.80 × 10⁵ comes from using ω₀ = 600 with no rpm conversion and also dropping the 2π from α: 600²/2 = 1.80 × 10⁵. Converting rpm to rad/s gives ω₀ = 20π rad/s.
MCQ 7CalculationPractice
A motor accelerates a disc from 3.00 × 10² rpm to 9.00 × 10² rpm in 10 s at constant angular acceleration. What is the angular displacement during this interval?
Show answer and why every option is right or wrong
Answer: B. Convert: ω₀ = 300 × 2π/60 = 10π rad/s, ω = 900 × 2π/60 = 30π rad/s. Use θ = ½(ω₀ + ω)t = ½(10π + 30π)(10) = 200π rad (NCERT Class 11 Physics, Chapter 6, page 105).
Why A is wrong: A is wrong because 100π results from using only ω₀t = 10π × 10, ignoring the acceleration component over the interval.
Why C is wrong: C is wrong because 6000 comes from averaging 300 and 900 rpm (getting 600), then multiplying by 10 s — without converting rpm to rad/s. The result has wrong units.
Why D is wrong: D is wrong because 3000 = 6000/2, an attempt to correct for the averaging formula but still without the rpm-to-rad/s conversion.
MCQ 8Concept TrapPractice
The rotational kinetic energy of a body rotating about a fixed axis is given by KE_rot = ½Iω². If ω is mistakenly entered in rpm instead of rad/s, by what factor is the calculated KE_rot wrong?
Show answer and why every option is right or wrong
Answer: C. If ω_actual = (2π/60) × ω_rpm, then using ω_rpm directly gives KE_wrong = ½I(ω_rpm)². The correct value is ½I[(2π/60)ω_rpm]² = ½Iω_rpm² × (2π/60)². So KE_wrong/KE_correct = 1/(2π/60)² = (60/2π)² = (30/π)² ≈ 91.2. The wrong answer is too large by (30/π)².
Why A is wrong: A is wrong because 60² = 3600 ignores the 2π in the conversion factor. The correct ratio involves (30/π)² ≈ 91.2, not 3600.
Why B is wrong: B is wrong because (2π/60)² ≈ 0.011 is the factor by which the correct KE is smaller than the raw-rpm KE — it describes the ratio in the wrong direction. The calculated value is too LARGE, not too small.
Why D is wrong: D is wrong because the moment of inertia I has units kg·m² and does not depend on the unit of ω; using rpm instead of rad/s produces a numerically wrong KE.
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Rotational Equations of Motion: quick recall before you leave
How do you solve a Rotational Equations of Motion question? A worked example
Pattern: Flywheel undergoing uniform angular acceleration (based on the in-scope PYQ pattern for this topic).
- 1
Given
A flywheel starts from rest and reaches 1.80 × 10³ rpm in 6.0 s under constant angular acceleration.
- 2
Required
(a) Angular acceleration α in rad/s².
(b) Number of revolutions completed in 6.0 s. - 3
Concept
Rotational kinematic equations under constant α — the rotational analogues of linear kinematics (NCERT Class 11 Physics, Chapter 6, page 105).
- 4
Formula
ω = ω₀ + αt and θ = ω₀t + ½αt².
- 5
Substitution
Unit conversion first: ω = 1800 × (2π/60) = 60π rad/s. ω₀ = 0 (starts from rest).
(a) α = (ω − ω₀)/t = 60π/6.0 = 10π rad/s².
(b) θ = 0 + ½ × 10π × (6.0)² = ½ × 10π × 36 = 180π rad. - 6
Calculation
(a) α = 10π ≈ 31.4 rad/s².
(b) θ = 180π rad. Number of revolutions = 180π/(2π) = 90 revolutions.
Note on exact constants: The factor 2π in the rpm conversion and the divisor 2π for converting radians to revolutions are exact mathematical constants. The counting numbers 6 (time) and 1800 (rpm) are given values treated as exact for this problem. These do not limit significant figures — the precision is set by the physical measurements. - 7
Final answer
(a) α = 10π rad/s² ≈ 31 rad/s² (2 significant figures, matching the precision of 6.0 s).
(b) The flywheel completes 90 revolutions in 6.0 s. - 8
Common trap
If you forget to convert 1800 rpm to rad/s, you get α = 1800/6.0 = 300 "rad/s²" — which is off by a factor of 2π/60 from the correct answer. This matches the rpm-to-rad/s trap documented for this topic. Always convert before substituting.
- 9
Similar NEET-style question
A turbine blade accelerates uniformly from 3.00 × 10² rpm to 1.50 × 10³ rpm in 10 s. Find (a) the angular acceleration and (b) the total angle turned in radians during this interval. (Answer: convert both rpm values to rad/s first, then apply the kinematic equations.)
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What to remember before solving Rotational Equations of Motion questions
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. 119Which Rotational Equations of Motion formulas do you need for NEET?
1 formula — click to collapse
Rotational kinematic equations (constant alpha)
Rotational analogues of linear kinematic equations under constant angular acceleration.
| Symbol | Quantity | SI Unit |
|---|---|---|
| omega | angular velocity | rad/s |
| alpha | angular acceleration | rad/s^2 |
| theta | angular displacement | rad |
| t | time | s |
Valid when
- Constant alpha
- Single rotation axis
Where do students lose marks on Rotational Equations of Motion?
These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.
2 items — click to collapse
Category: Unit Conversion
Student plugs rpm directly into formulas requiring rad/s. 1 rpm = 2π/60 rad/s.
When it triggers
Question gives ω in rpm and asks for kinematic quantities in SI units.
How to avoid
Convert: ω(rad/s) = (2π/60) × rpm. Always check units before substituting.
Root cause: unit error
Correction
Convert: ω(rad/s) = (2π/60) × ω(rpm). For example, 1200 rpm = 1200 × 2π/60 = 125.66 rad/s.
More in System of Particles and Rotational Motion: 5 exam traps and mistakes · 7 formulas · 3 question patterns from its other lessons.
Rotational Equations of Motion questions from past NEET papers
1 question from NEET 2022. Answers verified against NTA official keys. — click to collapse
NEET 2022
1104π
22π
34π
412π
NTA Answer: Option 3(final)
All 11 past-paper questions from System of Particles and Rotational Motion →
How does NEET ask about Rotational Equations of Motion?
1 recurring pattern from past papers — click to collapse
Flywheel undergoing uniform angular acceleration; given initial/final omega and time, find alpha or theta.
Direct ApplicationEasy
Common distractors
forgets conversion rpm to rad s
Treats rpm as rad/s without 2*pi/60 conversion
Sources
NCERT refs: Class 11 Physics Chapter 6, p.105 | Class 11 Physics Chapter 6, p.106
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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