Chapter 28 · Class 11-12 & JEE/NEET
Work, Energy & Power
35 topics in 9 parts
Work–energy theorem Spring potential energy Work by a Constant Force Work by a Variable Force Force-Displacement Graph Kinetic Energy
Key ideas
4. Systematic Comparison & Parameter Classifications
| Body Shape | Axis of Rotation | Moment of Inertia (I) | Shape Factor (k² / R²) |
|---|---|---|---|
| Thin Ring / Hollow Cylinder | Central Axis Perpendicular to Plane | M R² | 1.0 (Slowest Down Incline) |
| Solid Disc / Solid Cylinder | Central Axis Perpendicular to Plane | (1/2) M R² | 0.50 |
| Solid Sphere | Diameter Axis | (2/5) M R² | 0.40 (Fastest Down Incline) |
| Spherical Shell (Hollow) | Diameter Axis | (2/3) M R² | 0.67 |
| Uniform Rod (Length L) | Through Center Perpendicular to Length | (1/12) M L² | L² / (12 R²) |
Exam Worked Example
Problem: A solid sphere and a solid cylinder of equal mass M and radius R roll down the same inclined plane without slipping from rest. Find the ratio of their accelerations down the incline.
● Step 1: Formula for linear acceleration in pure rolling: a = (g sin θ) / (1 + k²/R²).
● Step 2: For solid sphere, k²/R² = 2/5 = 0.4. Therefore, a_sphere = (g sin θ) / (1 + 2/5) = 5/7 g sin θ ≈ 0.714 g sin θ.
● Step 3: For solid cylinder, k²/R² = 1/2 = 0.5. Therefore, a_cyl = (g sin θ) / (1 + 1/2) = 2/3 g sin θ ≈ 0.667 g sin θ.
● Step 4: Ratio a_sphere / a_cyl = (5/7) / (2/3) = (5 * 3) / (7 * 2) = 15 / 14 ≈ 1.07. The solid sphere reaches the bottom first!
Checkpoint
1. When a ballet dancer pulls her arms inward during a spin on smooth ice, what happens to her kinetic energy?
All 35 topics in Work, Energy & Power
Work
- Nature of Work Done
- Done by Constant Force
- Done by Variable Force
- Done by Different Forces
- Frame of Reference Dependence
- Zero Work Conditions
Work-Energy Theorem
- Application to Constant Force
- Application to Variable Force
- Non-Inertial Frame Application
- Spring & Connected Mass Systems
Conservative & Non-Conservative Forces
- Conservative Forces
- Non-Conservative Forces
- Path Independence & Work Done by Friction
Potential Energy
- Change in Potential Energy
- Gravitational Potential Energy
- Elastic Potential Energy Stored in a Spring
- Three-Dimensional Formula for Potential Energy
- Relation Between Force & Potential Energy
Conservation of Mechanical Energy
- Principle of Energy Conservation
- Energy Dissipation with Friction
- Pendulum & Pulley Energy Analysis
- Chain & Rope Energy Systems
Equilibrium & Potential Energy Curves
- Stable, Unstable & Neutral Equilibrium
- Potential Energy Curve Analysis
- Particle Motion in Potential Fields
Kinetic Energy & Linear Momentum Relation
- KE-Momentum Calculations
- Percentage Changes in KE & Momentum
- Stopping Distance & Penetration Retardation
Motion in a Vertical Circle
- Velocity & Tension at Critical Points
- Condition for Oscillation or Leaving Circle
- Critical Speed for Loop Completion
Power
- Average & Instantaneous Power
- Constant Power Motion
- Variable Power
- Machines & Pumps Power Output