NEET Physics — Rotational Motion

Work, Energy and Power for Rotating Body – Complete Notes, Revision, Important Questions & Downloads

This topic extends work, energy, and power concepts to rotating bodies. The single TOC subtopic Work and Kinetic Energy covers the rotational analogues: work done by torque W = ∫τ dθ, rotational kinetic energy KE_rot = ½Iω², work-energy theorem for rotation (W_net = ΔKE_rot), and power P = τω. The relation τ = dL/dt is also tested in this context. NEET questions in this area typically involve calculating the work done to bring a rotating body to rest, or the power delivered by a constant torque.

⬇ Download Notes PDF View Important Questions →

1 SubtopicMedium FrequencyRotational Analogues

Expected QuestionsQ

Typically 1 NEET question per year on rotational KE, work done by torque, or power in rotational motion.

Time Required⏱

1–2 hours

One session to learn the rotational analogues and one session to practise numerical problems combining W = τθ with KE = ½Iω².

Difficulty⚡

Medium

Direct analogies with linear motion make the formulas easy to learn; the challenge is correctly identifying I and ω from the problem statement.

NRI USA Curriculum GapUS

Low

AP Physics C covers rotational work and power in detail. AP Physics 1 covers rotational KE in the context of rolling motion.

1Subtopics

8+Practice Questions

4Free Downloads

1–2 hrsPrep Time

⬇ Get Free Downloads

NEET Weightage — Work, Energy and Power for Rotating Body

Rotational Motion (Chapter 7)

NEET Year	Questions from this Topic	Bar	Marks
2024	1	1 Q	4
2023	1	1 Q	4
2022	0	0 Q	0
2021	1	1 Q	4
2020	1	1 Q	4
2019	0	0 Q	0
6-Year Total (2019–2024)	3–5		12–20

Work done by torque W = τθ (constant torque) or W = ∫τ dθ — analogous to W = Fd for linear motion.
Power P = τω — the rotational analogue of P = Fv. NEET may give ω and torque and ask for instantaneous power.
Work-energy theorem for rotation: W_net = ½Iω₂² − ½Iω₁². NEET uses this to find work required to change rotational speed.

📊

~0.7

Avg Questions / Year

🎯

12–20

Total Marks (6 yrs)

📈

Direct

Pattern

⚠️

Medium

Difficulty

Exam Strategy for Work, Energy and Power (Rotational)

Map every linear formula to its rotational analogue W = Fd → W = τθ (work by torque). KE = ½mv² → KE_rot = ½Iω². P = Fv → P = τω. Impulse = FΔt → Angular impulse = τΔt = ΔL. Once mapped, solve rotational problems at the same speed as linear problems.

Apply the work-energy theorem for rotation W_net = ΔKE_rot = ½Iω₂² − ½Iω₁². For a body spinning up from rest (ω₁ = 0): W = ½Iω². For braking a spinning body to rest (ω₂ = 0): W = −½Iω₁² (work done by braking force = loss in rotational KE).

For power problems with constant torque and constant ω P = τω. If ω is changing over time under a constant torque, the instantaneous power P = τω(t) changes with time. The average power over a time interval = W/t = τΔθ/t = τω_avg.

Download Study Notes — Work, Energy and Power for Rotating Body

PDF · Cheat Sheet · MCQ Set · PYQ

📘

Rotational Work and Energy — Full Notes

Complete notes covering the rotational analogues table (linear vs rotational), derivations of W = τθ and KE = ½Iω², work-energy theorem for rotation, power equation P = τω, and 6 worked NEET-style examples.

1 subtopicAnalogy tableWorked examples

Download PDF

📗

Rotational Work and Energy — Formula Sheet

One-page reference: W = τθ, W = ∫τ dθ, KE_rot = ½Iω², W_net = ΔKE_rot, P = τω, τ = dL/dt, full linear-to-rotational analogy table.

1 pageAnalogy table

Download PDF

📙

Rotational Work and Energy — MCQ Practice

10 NEET-style MCQs on work done by torque, rotational KE, power in rotation, and work-energy theorem applications for rotating bodies.

10 MCQsDetailed solutions

Download PDF

📕

Rotational Work and Energy — NEET-Style PYQ Practice

NEET-style practice questions on work done to accelerate/decelerate a rotating body, power from torque, and combining rolling KE with work-energy theorem.

NEET-styleAnswer key included

Download PDF

Subtopics in Work, Energy and Power for Rotating Body

2-Column Table

Column A	Column B
Work and Kinetic Energy↗

Rapid Revision — Work, Energy and Power for Rotating Body

Concept → Trap → Example

1) Work and Kinetic Energy

Rotational Analogues

Work by torque: W = τθ (constant τ) or W = ∫τ dθ. Rotational KE: KE_rot = ½Iω². Work-energy theorem: W_net = ½Iω₂² − ½Iω₁². Power: P = τω. Angular impulse: J_ang = τΔt = ΔL.

The energy, which a body has by virtue of its rotational motion is called rotational kinetic energy — it is ½Iω², directly analogous to ½mv² for translational motion.
For a body that both translates and rotates (rolling), total KE = ½mv² + ½Iω² = ½mv²(1 + K²/R²) — both terms must be included in energy conservation equations.
Common NEET trap: computing W = τ × (angle in degrees) instead of τ × (angle in radians). Always convert angles to radians before computing rotational work: 1 revolution = 2π rad, 1° = π/180 rad.

Example (NEET-style)A flywheel of MI = 2 kg·m² accelerates from ω₁ = 5 rad/s to ω₂ = 15 rad/s under a constant torque. Work done = ΔKE = ½×2×(225 − 25) = 200 J. If this took θ = 40 rad, then τ = W/θ = 200/40 = 5 N·m. Power at ω₂: P = τω₂ = 5×15 = 75 W.

US Curriculum Gaps — Work, Energy and Power for Rotating Body

Students from the US system studying for NEET should note these specific coverage gaps:

AP Physics C covers rotational work and power; AP Physics 1 covers only rotational KE

AP Physics C Mechanics explicitly derives W = τθ and P = τω. AP Physics 1 only encounters rotational KE in the context of rolling without slipping (½Iω²) without the full work formalism. NEET tests all three: W = τθ, KE = ½Iω², and P = τω.

Explicitly memorise W = τθ as the rotational analogue of W = Fd — the derivation (W = ∫F·ds = ∫F·r dθ = ∫τ dθ) provides intuition for why this form is correct.
For constant torque: W = τθ exactly. For variable torque, integrate; NEET typically uses constant torque cases.
P = τω appears in NEET questions about motors: 'A motor produces torque 50 N·m at 100 rpm. What is its power?' Ans: P = 50 × (100 × 2π/60) = 50 × 10.47 ≈ 524 W.

The angle-in-radians requirement for rotational work is less emphasised in US courses

The formula W = τθ requires θ in radians — not degrees or revolutions. US courses sometimes present problems in rpm or degrees without explicitly emphasising the radians requirement. NEET always uses radians internally.

Conversion: 1 revolution = 2π rad. N revolutions = 2πN rad. Angular speed in rpm: ω = 2πN/60 rad/s.
Always convert given angle/revolution data to radians before substituting into W = τθ or any angular kinematic formula.
A body rotating at 300 rpm for 5 s: θ = ω × t = (300 × 2π/60) × 5 = 10π × 5 = 50π rad ≈ 157 rad.

NEET-Style Practice Questions — Work, Energy and Power (Rotational)

5 NEET-style questions

1A flywheel of moment of inertia 5 kg·m² is rotating at 10 rad/s. What work must be done to bring it to rest?Work-Energy Theorem

500 J

250 J

100 J

50 J

Work done to bring it to rest = ΔKE = KE_final − KE_initial = 0 − ½Iω² = −½×5×100 = −250 J. The negative sign indicates work is done against the rotation (braking work). The magnitude = 250 J must be supplied by the braking mechanism. The trap is computing ½×5×10 = 25 J (forgetting to square ω).

2A motor exerts a constant torque of 40 N·m. What is the power output when the angular velocity is 5 rad/s?Power = τω

8 W

200 W

45 W

400 W

P = τω = 40 × 5 = 200 W. This is the instantaneous power at the moment ω = 5 rad/s. If ω were 10 rad/s with the same torque, P = 400 W. Power increases linearly with angular velocity for constant torque.

3A torque of 20 N·m acts on a body rotating about a fixed axis. The body rotates through 8 revolutions. How much work is done?Work by Torque

160 J

1005 J

320 J

2010 J

θ = 8 revolutions = 8 × 2π = 16π rad. W = τθ = 20 × 16π = 320π ≈ 1005 J. The trap is using θ = 8 directly and computing W = 20 × 8 = 160 J — this fails because θ must be in radians, not revolutions.

4The rotational kinetic energy of a disc (I = 0.5 kg·m²) rotating at 4 rad/s equals the translational kinetic energy of a particle of mass m moving at 2 m/s. What is m?KE Equivalence

2 kg

1 kg

4 kg

0.5 kg

KE_rot = ½Iω² = ½×0.5×16 = 4 J. KE_trans = ½mv² = 4 J → ½m×4 = 4 → m = 2 kg. The key step is computing ½Iω² correctly: I = 0.5, ω = 4, ω² = 16, so ½×0.5×16 = 4 J.

5A grindstone (I = 2 kg·m²) is initially at rest and is rotated by a constant torque of 10 N·m for 5 revolutions. What is the final angular velocity?Work-Energy + KE

10 rad/s

√(100π) ≈ 17.7 rad/s

5π rad/s

√(50) ≈ 7.07 rad/s

W = τθ = 10 × 5 × 2π = 100π J. By work-energy theorem: ½Iω² = 100π → ½×2×ω² = 100π → ω² = 100π → ω = √(100π) ≈ √314 ≈ 17.72 rad/s. The trap is using θ = 5 (not 10π), giving ω² = 50 and ω ≈ 7.07 rad/s.

Practice Questions — Work, Energy and Power (Rotational)

Click "Reveal Answer" after attempting

1A ceiling fan (I = 0.8 kg·m²) starts from rest and reaches ω = 10π rad/s in 20 s under constant torque. Find the torque and the work done.

τ = 4π/5 N·m, W = 200π² J

τ = 2 N·m, W = 400π² J

τ = π/4 N·m, W = 100 J

τ = 2π N·m, W = 400 J

👁 Reveal Answer

Answer: τ = 0.4π N·m ≈ 1.26 N·m; W = 400π² ≈ 3948 J. α = Δω/Δt = 10π/20 = π/2 rad/s². τ = Iα = 0.8 × π/2 = 0.4π N·m. W = ΔKE = ½Iω² = ½×0.8×(10π)² = 0.4×100π² = 40π² ≈ 395 J. Also W = τθ = 0.4π × (average ω × t) = 0.4π × (5π × 20) = 40π² ✓.

2An engine produces 80 kW at 2000 rpm. What torque does it exert?

382 N·m

191 N·m

764 N·m

40 N·m

👁 Reveal Answer

Answer: τ = P/ω = 80000 / (2000 × 2π/60) = 80000 / (209.4) ≈ 382 N·m. Convert rpm to rad/s: ω = 2000 × 2π/60 = 200π/3 ≈ 209.4 rad/s. Then τ = P/ω = 80000/209.4 ≈ 382 N·m.

3A disc of mass 1 kg and radius 0.5 m rolls without slipping at v = 4 m/s. What is its total kinetic energy?

8 J

12 J

6 J

16 J

👁 Reveal Answer

Answer: 12 J. KE = ½mv²(1+K²/R²) = ½×1×16×(1+½) = 8×1.5 = 12 J. Breakdown: KE_trans = ½×1×16 = 8 J; KE_rot = ½×(½×1×0.25)×(4/0.5)² = ½×0.125×64 = 4 J. Total = 12 J ✓.

4How much work is required to increase the angular speed of a rotating disc (I = 3 kg·m²) from 6 rad/s to 10 rad/s?

96 J

48 J

192 J

80 J

👁 Reveal Answer

Answer: 96 J. W = ΔKE = ½×3×(100 − 36) = ½×3×64 = 96 J.

Physics — Rotational Motion Revision Checklist

Check off chapters as you revise

Use this section for quick chapter tracking before mocks, part tests, and final NEET revision.

Work and Kinetic Energy: Derive the rotational analogy table and apply W = τθ and KE = ½Iω² to two problemsProblem 1: given torque and angle in revolutions, find work done (convert to radians first). Problem 2: given initial and final ω and MI, find work done using the work-energy theorem ΔKE = W_net. Cross-check by computing W = τθ if θ is given.

FAQ — Work, Energy and Power for Rotating Body

Notes · Downloads · Revision · Important Questions

Why is the formula for work done by torque W = τθ and not W = τ × arc length?

Work = force × displacement in the direction of force. For rotation, the force is tangential (F_t = τ/r) and the arc length is ds = r dθ. So dW = F_t × ds = (τ/r) × r dθ = τ dθ. Integrating: W = ∫τ dθ = τθ (constant torque). Note that the radius r cancels — work by torque depends only on τ and θ (in radians), not on the radius.

Can the rotational KE ever exceed the translational KE for a rolling body?

For rolling without slipping, KE_rot/KE_trans = K²/R². Since K²/R² ≤ 1 for all standard bodies (maximum value is 1 for a ring), KE_rot ≤ KE_trans always. The ring is the case where KE_rot = KE_trans (50/50 split). For all other standard rolling bodies, KE_rot < KE_trans.

What is the relationship between angular impulse and angular momentum?

Angular impulse = τ × Δt = ΔL (change in angular momentum). This is the rotational analogue of linear impulse = F × Δt = Δp. If a constant torque τ = 8 N·m acts for 3 s, the angular impulse = 24 kg·m²/s, and the body gains 24 kg·m²/s of angular momentum. If I = 4 kg·m², then Δω = ΔL/I = 24/4 = 6 rad/s.

Is the path taken by a rotating body relevant to the work done by a constant torque?

No — for constant torque, W = τθ depends only on the total angle rotated (θ), not on the path or the time taken. This is analogous to W = Fd for a constant force depending only on displacement. Torque is a conservative concept for constant torque problems: the work done in going from θ₁ to θ₂ is τ(θ₂ − θ₁) regardless of the path.

How is rotational work different from the torque × distance formula?

Torque × distance (τ × r) is not work — it has units N·m² (force × distance²). Rotational work is W = τ × θ, where θ is the dimensionless radian angle, giving units N·m = J (energy). The formula W = τθ is analogous to W = Fd (force × linear displacement in metres), not to torque × radius.

What is the analogy between power in linear and rotational motion?

Linear: P = F·v (force × velocity). Rotational: P = τ·ω (torque × angular velocity). This analogy holds because P = dW/dt = τ dθ/dt = τω. For a motor producing constant torque τ, power increases linearly with angular velocity ω — as the motor speeds up, it delivers more power even with the same torque. Maximum power at maximum safe ω.

Can rotational kinetic energy be converted to translational kinetic energy?

Yes — a common example is a spinning gyroscope or a rolling body. In rolling without slipping, rotational and translational KE are simultaneously present and both are derived from the same reduction in potential energy (mgh) as the body rolls down a slope. A spinning top with gyroscopic precession converts some rotational KE into precessional (translational) motion of the axis. In a braking system, rotational KE of the flywheel is converted to heat via friction.

If a torque does 100 J of work and the body rotates through 5 revolutions, what is the torque?

θ = 5 revolutions × 2π rad/revolution = 10π rad. τ = W/θ = 100 / (10π) = 10/π ≈ 3.18 N·m. The key step is converting revolutions to radians before dividing. If you use θ = 5 (raw revolutions), you get τ = 20 N·m — this is wrong by a factor of 2π.

For NRI / OCI / U.S.-Based Families

NEET NRI Counseling & Admission eBook Download

A practical guide covering sponsor rules, document checklist, verification traps, NRI quota reality, and step-by-step counselling flow. Designed to prevent last-minute rejections and wrong choice filling.

Sponsor + Proof ClarityDocuments ChecklistState-wise Traps

↓ Download eBook (PDF)→ See What's Inside

Tip: Keep this eBook open during verification + choice filling week for quick cross-checking.

NEET Prep (India + NRI-USA)

Schedule Trial Session For NEET Prep

Get a short diagnostic + study roadmap: syllabus gaps (NCERT vs U.S. curriculum), weak chapters, and the exact weekly plan needed to improve accuracy under time.

Gap MappingWeekly PlanAccuracy Fix

→ Book Trial Session → WhatsApp Us

Best for: Students in Grade 10–12 (U.S. / India) who want a clear NEET timeline and daily practice structure.

Work, Energy and Power for Rotating Body

Work, Energy and Power for Rotating Body – Complete Notes, Revision, Important Questions & Downloads

1) Work and Kinetic Energy

AP Physics C covers rotational work and power; AP Physics 1 covers only rotational KE

The angle-in-radians requirement for rotational work is less emphasised in US courses

Physics — Rotational Motion Revision Checklist

NEET NRI Counseling & Admission eBook Download

Schedule Trial Session For NEET Prep

Work and Kinetic Energy

Subtopics

Work and Kinetic Energy

NEET > Physics > System of Particles and Rigid Body Chapters

Comments

Leave a comment

Comments (0)

Work, Energy and Power for Rotating Body

Overview content

Work, Energy and Power for Rotating Body – Complete Notes, Revision, Important Questions & Downloads

1) Work and Kinetic Energy

AP Physics C covers rotational work and power; AP Physics 1 covers only rotational KE

The angle-in-radians requirement for rotational work is less emphasised in US courses

Physics — Rotational Motion Revision Checklist

NEET NRI Counseling & Admission eBook Download

Schedule Trial Session For NEET Prep

Work and Kinetic Energy

Subtopics

Work and Kinetic Energy

NEET > Physics > System of Particles and Rigid Body Chapters

Comments

Leave a comment

Comments (0)