Define center of mass. What is the effect of mass distribution in a body on its center of mass?

The center of mass is the point in a body or system where the total mass of the body can be considered to be concentrated. It is the weighted average of the positions of all the particles that make up the body, weighted by their masses.

Effect of mass distribution:

  • If the mass of the body is symmetrically distributed, the center of mass lies at the geometric center of the body.
  • If the mass distribution is uneven, the center of mass shifts toward the side with greater mass. For example, in an irregularly shaped object, the center of mass would be closer to the denser part of the object.

The center of mass plays a crucial role in understanding the motion of an object, especially when it undergoes rotation or translation. For example, in a rotating object, the center of mass moves in a straight line while the object rotates about its center of mass.

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