# Centre Of Mass Concept Used In Reality!

I want to know a brief about centre of mass.

We know that centre of mass defines the whole trajectory of system, but I came to a question while solving one derivation regarding it in its equation, that, as centre of mass of the thin semicircular wire of radius r [edit for clarity: a thin wire bent into a semi-circular shape] is $$(0,2r/\pi)$$. I am assuming that the center of the ring lies at the origin of coordinates and the ring itself lies completely above the $$x$$-axis.

When I assume $$r$$ some value, suppose 4, then its centre of mass became $$(0,2.54).$$ But considering this semi-circular shape has no mass of wire at that location, because its radius is 4, then how that point be its centre of mass? How it will define in physical manner? Also, is centre of mass a balance mass point?

• Possible duplicate: physics.stackexchange.com/questions/355987/… Jul 3, 2019 at 13:40
• Thanku for clearing doubt. Jul 3, 2019 at 14:00
• Possible duplicate of Applying force on centre of mass of a body which lies outside the body Jul 3, 2019 at 14:04
• Think of the centre-of-mass as the point that represents the entire object, if you had to squeeze it into a point. The centre-of-mass of a donut is in the hole in the middle - there is no actual mass there, but all the mass around this point "averages out", so to say, to this point. Jul 3, 2019 at 14:37