LMR — Motion in a Plane (NCERT Ch.3)

Formulas, tips, mistakes & essential notes — SharpRevise style

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Core Definitions

Strong Hold

Vector: magnitude + direction (displacement, velocity, acceleration)
Displacement vs Distance: vector vs scalar
Position vector: r = xi + yj; unit vectors i,j

vectordisplacement

Kinematics — Constant Acceleration

Strong Hold

v = u + at

s = ut + ½at²

v² = u² + 2as

Apply separately to x and y components

v,u,a,scomponents

Projectile Motion

Needs Attention

T = (2u sinθ)/g

H = (u² sin²θ)/(2g)

R = (u² sin2θ)/g

Resolve velocity into components: ux = u cosθ, uy = u sinθ

R,H,Tcomponents

Relative Motion & Vectors

Needs Attention

vAB = vA − vB
Vector addition tip-to-tail
Resolve into perpendicular components using i,j

vABi,j

Circular Motion

Frequent Mistakes

a_c = v²/r = ω² r

a_t = r α

Direction inward; total accel = tangential + radial vector sum

a_cω

Common Mistakes

Frequent Mistakes

Mixing speed & velocity
Projectile formulas without resolving components
Centripetal accel points inward
Sign errors: upward +, downward -

signscomponents

Quick Solving Tips

Needs Attention

Resolve vectors into x & y first
Choose axes smartly; align with motion
Check units: m/s, s, m; g=9.8
Use Pythagoras for perpendicular components

resolveunits

Handy Formula Pack

v = u + at • s = ut + ½at² • v² = u² + 2as • R=(u² sin2θ)/g • T=(2u sinθ)/g

Memorize symbols, not wordy form — saves seconds in exams

memorize

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