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Equilibrium and the Force of Gravity

Equilibrium and the Force of Gravity - Equilibrium and the...

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Equilibrium and the Force of Gravity Figure 13.1. Weight of an object balanced by a single force. Figure 13.1 shows a body of arbitrary shape balanced by a single force. The origin of the coordinate system is defined such that it coincides with the center of gravity of the object, which is the point upon which the balancing force acts. An object that is supported at its center of gravity will be in static equilibrium, independent of the orientation of the object. If the body is in equilibrium, the net force acting on it must be zero. Figure 13.1 shows that Since the body is in equilibrium and therefore In obtaining this result we have assumed that the gravitational acceleration is the same for every point of the body . The net torque acting on the body is given by Since the body is in static equilibrium and therefore This shows that r cm = 0 or r cm is parallel to g. We conclude that for a body to be in equilibrium, its center of mass must coincide with its center of gravity .
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