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Physics
Classical Physics
Mechanics
Why do objects always rotate about their centre of mass?
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[QUOTE="Delta2, post: 6357952, member: 189563"] There are two theorems in classical mechanics involving rigid body motion (translation and rotation). [LIST=1] [*]The sum of external forces acting on a rigid body (regardless where exactly these forces are applied and if they are tangential or not) equals the mass of the rigid body times the (translational) acceleration of its center of mass. Mathematically $$\sum \vec{F_{ext}}=m\vec{a_{CM}}$$ [*]The sum of external torques (around any reference point) acting on a rigid body equals the moment of inertia (around the same reference point) of the rigid body times its angular acceleration (here the torques depend on where exactly the forces are applied and if they are tangential). Mathematically $$\sum \vec{T_{ext}}=I\vec{\alpha}$$ [/LIST] These two theorems, gives us the result that when an external force is applied in a rigid body, will have in the general case both a translational effect (accelerated movement of the CM of the body) and a rotational effect (angular acceleration) because in the general case the applied force will have a torque which is not zero (not around all possible reference points). The first theorem also tell us that the rotation of a body will always be around its CM when there are no external forces applied, because in this case it will be $$0=\sum F=ma_{CM}\Rightarrow a_{CM}=0$$. If the rotation was around another point , then the CM would also rotate around that point which would mean that ##a_{CM}\neq 0##, contradicting that ##a_{CM}=0##. [/QUOTE]
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Classical Physics
Mechanics
Why do objects always rotate about their centre of mass?
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