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Cheat sheet · JEE Preparation Physics

Laws of Motion cheat sheet

The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.

JEE · Physics

Cheat sheet

Class 11 · Chapter 4Laws of Motion

Inertia → F = dp/dt → Action–reaction: Newton's 1-2-3.

1. Newton's Laws

First law

A body stays at rest or in uniform motion unless an external force acts (inertia).

Second law

F⃗=dp⃗dt=ma⃗\vec F = \dfrac{d\vec p}{dt} = m\vec a

Third law

To every action there is an equal and opposite reaction, acting on different bodies.

2. Momentum & Impulse

p⃗=mv⃗\vec p = m\vec vJ⃗=F⃗ Δt=Δp⃗\vec J = \vec F\,\Delta t = \Delta \vec p

Conservation of momentum: with no external force, total momentum stays constant (recoil of a gun, rocket).

3. Friction

fs≤μsNf_s \le \mu_s Nfk=μkNf_k = \mu_k Nμk<μs\mu_k < \mu_s
  • Angle of repose: tan⁡θ=μs\tan\theta = \mu_s.
  • Rolling friction ≪ sliding friction (ball bearings, wheels).

4. Circular Motion

Fc=mv2rF_c = \dfrac{mv^2}{r}
  • Flat road: vmax=μsrgv_{max} = \sqrt{\mu_s r g}.
  • Banked road: vmax=rgμs+tan⁡θ1−μstan⁡θv_{max} = \sqrt{rg\dfrac{\mu_s + \tan\theta}{1 - \mu_s\tan\theta}}; with μs=0\mu_s = 0, vo=rgtan⁡θv_o = \sqrt{rg\tan\theta}.

5. Lift Problems

Lift motionApparent weight
At rest / uniform vmg
Accelerating up (a)m(g + a)
Accelerating down (a)m(g − a)
Free fall0

6. Key Points

  • Draw a free-body diagram for each body.
  • Action and reaction never cancel (different bodies).
  • Equilibrium: vector sum of forces = 0.
  • Mass is a measure of inertia.

Remember: F = dp/dt | Impulse = Δp | μ_s N | mv²/r

Laws of Motion: questions and notes

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