The description of the motion of the center of mass is neccessary but not sufficient to define the motion of a body or a system of particles. Specifically, Eqn. (3.9) provides no information on the rate of rotation of a solid body or the relative motion of particles in a system of particles. Clearly, a mere summation is not enough to capture all the very important parameters of motion. What is nature's law governing the rotation of a body? Intuitively, we know that whenever a force is applied further away from a pivot point, the better is its capacity to induce rotation. A good example of this is the positioning of door knobs. They are located at the free edge of the door rather than being close to the edge hinged to the wall. This way the distance between the axis of rotation and the force one exerts on the door when one wants to swing it open is maximized.
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The use of dumbbells gives you a much more comprehensive strengthening effect because the workout engages your stabilizer muscles, in addition to the muscle you may be pin-pointing. Without all of the belts and artificial stabilizers of a machine, you also engage your core muscles, which are your body's natural stabilizers.