Calculating the center of massm,r +m,r +m,r +.COMm +mz +m3 +
Calculating the center of mass . . 1 2 3 1 1 2 2 3 3 COM + + + + + + = m m m m r m r m r r
ExampleTwo particles with the same mass m.ri = (0, 0, 0) metresr = (2.0,0, 0) metresCOMmass=mmass=mx2.0 mm,ri+mzr2rcOMmi +m2
x y 2.0 m Example COM Two particles with the same mass m. 2.0,0,0 metres 0,0,0 metres 2 1 = = r r mass = m mass = m 1 2 1 1 2 2 COM m m m r m r r + + =
ExampleWhat if one of the particles has3 times the mass of the other?ri = (0,0,0)mr2 =(2.0,0,0) mmass= 3mmass=mx2.0 mmi+mzr2rcoMmi +m2
x y 2.0 m Example What if one of the particles has 3 times the mass of the other? 2.0,0,0 m 0,0,0 m 2 1 = = r r mass = m mass = 3m 1 2 1 1 2 2 COM m m m r m r r + + =
ExampleThe COM moves closer to themore massive particleri = (0,0,0) metresr = (2.0,0,0) metresmass = 3mCOMmass=mx2.0 mmi+m,rrcoMm +m2
x y 2.0 m Example The COM moves closer to the more massive particle. 2.0,0,0 metres 0,0,0 metres 2 1 = = r r mass = m mass = 3m 1 2 1 1 2 2 COM m m m r m r r + + = COM
ExampleThree particles with the same mass mVi = (0,0,0) metres2 = (2.0, 0, 0) metresCOMr2 = (2.0,1.5,0) metres1.5 m0x2.00 mmr +mzr +mgrsCOMm +m2 +ms
x y 2.00 m 1.5 m Example COM Three particles with the same mass m. 2.0,1.5,0 metres 2.0,0,0 metres 0,0,0 metres 2 2 1 = = = r r r 1 2 3 1 1 2 2 3 3 COM m m m m r m r m r r + + + + =