Why can the total force exerted on an object be taken as if a single force was applied on the center of mass?(adsbygoogle = window.adsbygoogle || []).push({});

I think at most the total force must be the sum of tiny equal forces uniformly distributed. The mass must at most be uniformly distributed too.

And this only matters when we start talking about rotational mechanics, right? i.e: Torques. So that the torque can be calculated as [itex]\tau[/itex]=[itex]R \times{F}_{T}[/itex]. But why is this true?

R being the vector of the position of the COM.

I think it can be explained this way:Using the known equation:

[itex]\boldsymbol{L}=\boldsymbol{L}_{CM}+\boldsymbol{L}_{spin}[/itex]

[itex]{L}_{CM}=[/itex] is the L of a point particle in the COM with mass M.

[itex]{L}_{spin}[/itex] is the L of body relative to it's center of mass.

Now by symmetry. Since [itex]{L}_{spin}[/itex] is on the center of mass it must be 0. There's an equal amount of tiny forces on each side of the body which makes the torque 0.

Can anyone just give me some insight into this? I just want to understand this basic clearly and there may be a simpler broader explanation.

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# Why can the total force be taken as if applied on the COM. (rotational mechanics?)

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