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Cheat sheet · JEE Preparation Physics

Motion in a Plane 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 3Motion in a Plane

Projectile: horizontal velocity constant, vertical motion is free fall.

1. Vectors

  • Resultant: R=A2+B2+2ABcos⁡θR = \sqrt{A^2 + B^2 + 2AB\cos\theta}, tan⁡α=Bsin⁡θA+Bcos⁡θ\tan\alpha = \dfrac{B\sin\theta}{A + B\cos\theta}.
  • Components: Ax=Acos⁡θA_x = A\cos\theta, Ay=Asin⁡θA_y = A\sin\theta.
  • Unit vector A^=A⃗/∣A⃗∣\hat{A} = \vec{A}/|\vec{A}|.
  • Triangle and parallelogram laws of vector addition.

2. Projectile Motion

Launched with speed uu at angle θ\theta to the horizontal:

T=2usin⁡θgT = \dfrac{2u\sin\theta}{g}H=u2sin⁡2θ2gH = \dfrac{u^2\sin^2\theta}{2g}
R=u2sin⁡2θgR = \dfrac{u^2\sin 2\theta}{g}Rmax=u2gR_{max} = \dfrac{u^2}{g} at 45∘45^\circ
y=xtan⁡θ−gx22u2cos⁡2θy = x\tan\theta - \dfrac{g x^2}{2u^2\cos^2\theta}

Range is the same for θ\theta and 90∘−θ90^\circ - \theta. Path is a parabola.

3. Uniform Circular Motion

v=ωrv = \omega rω=2πT=2πν\omega = \dfrac{2\pi}{T} = 2\pi\nuac=v2r=ω2ra_c = \dfrac{v^2}{r} = \omega^2 r

Speed is constant but velocity changes direction, so there is a centripetal acceleration towards the centre.

4. Key Points

  • At the top of the path, velocity is horizontal (u cos θ).
  • Acceleration of a projectile is g downward throughout.
  • Scalars + vectors cannot be added.
  • Relative velocity of rain: v_rm = v_r − v_m.

Remember: Resolve into x and y | T, H, R formulas | a_c = v²/r

Motion in a Plane: questions and notes

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