Mechanics & Gravitation
Kinematics, laws of motion, work-energy theorem, rotational dynamics, and gravitation
Key Concepts
- Kinematics: equations of motion apply only for uniform acceleration
- Newton's laws: net force produces acceleration (F = ma)
- Work–energy theorem: net work done equals change in kinetic energy
- Rotational motion: torque is the rotational analogue of force
- Gravitation: Kepler's laws govern planetary motion (T² ∝ r³)
Important Formulae
| Equations of motion | v = u + at; s = ut + ½at²; v² = u² + 2as |
| Newton's second law | F = ma |
| Work done | W = F·s·cosθ |
| Kinetic energy | KE = ½mv² |
| Torque | τ = Iα = r × F |
| Escape velocity | v_esc = √(2GM/R) |
Quick Tips
- Choose a sign convention for direction at the start and stick to it throughout.
- Work done by friction is always negative; it opposes relative motion.
- For rolling without slipping, total KE = ½mv² + ½Iω².
Sample Practice Questions
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The kinetic energy of a 2 kg body moving at 3 m/s is:
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Answer: 9 J
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A body starts from rest with a constant acceleration of 2 m/s². How far does it travel in 5 seconds?
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Answer: 25 m
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Using v = u + at with u = 0, a = 10 m/s² and t = 3 s, find v.
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Answer: 30 m/s
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The work done by a force acting perpendicular to the displacement is:
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Answer: Zero
Practice Questions
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What are the key concepts in Mechanics & Gravitation for JEE?
Kinematics: equations of motion apply only for uniform acceleration; Newton's laws: net force produces acceleration (F = ma); Work–energy theorem: net work done equals change in kinetic energy; Rotational motion: torque is the rotational analogue of force; Gravitation: Kepler's laws govern planetary motion (T² ∝ r³).
Which formulae are important for Mechanics & Gravitation in JEE?
Equations of motion: v = u + at; s = ut + ½at²; v² = u² + 2as; Newton's second law: F = ma; Work done: W = F·s·cosθ; Kinetic energy: KE = ½mv²; Torque: τ = Iα = r × F; Escape velocity: v_esc = √(2GM/R).
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