Centre of Mass
ICSE · Class 11 · Physics
All formulas from Centre of Mass in ICSE Class 11 Physics. Key equations, constants, and identities for board exam preparation.
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Formulas
2) Two-Particle System
(m1 + m2) r_cm = m1 r1 + m2 r2
r_cm = (m1 r1 + m2 r2) / (m1 + m2)
If r_cm = 0, then m1 r1 + m2 r2 = 0
3) n-Particle System and Continuous Body
r_cm = (1/M) Σ(mi ri)
x_cm = (1/M) Σ(mi xi), y_cm = (1/M) Σ(mi yi), z_cm = (1/M) Σ(mi zi)
x_cm = (1/M) ∫ x dm, y_cm = (1/M) ∫ y dm, z_cm = (1/M) ∫ z dm
r_cm = (1/M) ∫ r dm
dm = (m/l) dx
4) Uniform Rod and Non-Uniform Rod
x_cm = (∫0 to l x (m/l dx)) / (∫ dm) = (1/(2l))(l^2 - 0)
x_cm = l/2
x_cm = (2/3)L
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