Chapter 14 · Class 11-12 & JEE/NEET
Laws of Motion & Friction
62 topics in 15 parts
Newton's second law Kinetic friction Newton's First Law Newton's Second Law Newton's Third Law Impulse
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 62 topics in Laws of Motion & Friction
Concept & Classification of Force
- Concept of Force
- Classification of Force
- Contact Forces
Newton's Laws of Motion
- First Law of Motion
- Second Law of Motion
- Third Law of Motion
Free-Body Diagrams
- Friction
- Normal Force
- Tension
- Weight
Equilibrium of a Particle
- Concurrent Forces
- Lami's Theorem
- Ladder Equilibrium
Applications of Newton's Laws
- Connected Bodies & Pushing Blocks
- Variable Force Problems
- Wedge Problems
Apparent Weight & Elevators
- Elevator Acceleration & Apparent Weight
- Weighing Machines & Spring Balances
Impulse & Momentum
- Impulse of Force
- Conservation of Linear Momentum
- Impulsive Forces & Collisions
- Variable Mass & Rocket Propulsion
- Force Exerted by Liquid Jet on a Wall
- Reaction Force Due to Ejection of Liquid
Pulley Systems & Atwood Machine
- Atwood Machine
- Pulley Systems
- Complex Pulley Systems
Constraint Relations
- String Constraints
- Pulley Constraints
- Wedge Constraints
- General Constraint Relations
- Pulley & Wedge Constraints
Frame of Reference & Pseudo Force
- Inertial Frame of Reference
- Non-Inertial Frame of Reference
- Pseudo Force
Spring Force & Combination of Springs
- Hooke's Law & Force Constant
- Force Constant of Composite Springs
- Cutting of Springs
- Spring-Block Systems & Equilibrium
Static & Kinetic Friction
- Analysis of Friction Force
- Types of Friction
- Direction of Frictional Force
- Static Friction & Coefficient of Friction
- Kinetic Friction
- Conveyor Belt
- Law of Limiting Friction
- Angle of Friction
- Pull Is Easier Than Push
Angle of Repose & Motion on Inclined Plane
- Angle of Repose & Sliding
- Motion on Inclined Planes
- Blocks in Contact on an Inclined Plane
Friction Acting on Multiple Surfaces
- Two-Block & Three-Block Systems
- Force Applied on Lower Block
- Force Applied on Upper Block
- Friction Between Blocks
Circular Motion Dynamics & Banking of Roads
- Uniform & Non-Uniform Circular Motion
- Centripetal Force
- Conical Pendulum
- Turning of Vehicles on Horizontal Circular Roads
- Banking of Roads
- Friction on Curved Surfaces
- Vertical Circular Motion