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Cheat sheet · Class 11 · CBSE · Science Physics

System of Particles and Rotational Motion cheat sheet

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

CBSE Class 11 · Physics

Cheat sheet

Chapter 6System of Particles and Rotational Motion

Rotational twins: F ↔ τ, m ↔ I, p ↔ L, v ↔ ω.

1. Centre of Mass

R⃗cm=∑mir⃗iM\vec R_{cm} = \dfrac{\sum m_i\vec r_i}{M}

CM moves as if all mass and external force were at that point. Internal forces don't change its motion.

2. Torque & Angular Momentum

τ⃗=r⃗×F⃗\vec\tau = \vec r\times\vec FL⃗=r⃗×p⃗\vec L = \vec r\times\vec p
τ⃗=dL⃗dt\vec\tau = \dfrac{d\vec L}{dt}L=IωL = I\omega

Conservation: if τext=0\tau_{ext} = 0, IωI\omega = constant (spinning skater pulls arms in → spins faster).

3. Linear vs Rotational

LinearRotational
xθ
vω\omega
mI=∑mr2I = \sum mr^2
F = maτ=Iα\tau = I\alpha
12mv2\tfrac12 mv^212Iω2\tfrac12 I\omega^2
P = FvP=τωP = \tau\omega

4. Moments of Inertia

Body (axis)I
Ring (centre, ⊥)MR2MR^2
Disc (centre, ⊥)12MR2\tfrac12 MR^2
Rod (centre, ⊥)112ML2\tfrac{1}{12}ML^2
Solid sphere (diameter)25MR2\tfrac25 MR^2

5. Equilibrium

  • Translational: net force = 0.
  • Rotational: net torque = 0.
  • Couple: equal, opposite, non-collinear forces — produces only rotation.

6. Key Points

  • Rolling KE = ½mv²(1 + k²/R²).
  • Radius of gyration: I = Mk².
  • Angular momentum is conserved when net external torque is zero.
  • Rotational equations mirror v = u + at etc. with ω, α, θ.

Remember: τ = Iα | L = Iω conserved | I of ring, disc, rod, sphere

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