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Finding the Center of Gravity

### 12.4: Finding the Center of Gravity

The center of gravity of a body is an imaginary point where the body's total weight is assumed to be concentrated, and the body is perfectly balanced. The center of the mass of a body is a point at which the whole of the mass of the body appears to be concentrated. If the acceleration due to gravity, g, has the same value at all points on a body, its center of gravity is identical to its center of mass. The center of gravity of homogeneous bodies such as a sphere, cube, or rectangular plate is at its geometric center, while the center of gravity of a right circular cylinder or cone is on its axis of symmetry. The center of gravity for complex bodies can be determined by hanging or swinging the body freely and using a three-step process.

For example, consider an irregularly shaped wooden plank having three holes at its corners. To determine the center of gravity of the plank, move or swing the plank freely when pivoted from three points X, Y, and Z on a rod.

1. First, suspend the wooden plank from point X and hang a vertical plumb line. Once the plumb line oscillates freely and reaches the equilibrium position, mark the point as “P” and draw a line XP on the object.
2. Similarly, suspend the wooden plank from Y, and when the plumb line comes to the equilibrium position, mark the line as YQ.
3. Repeat the same procedure by hanging the wooden plank from Z and mark the line as ZR.

The point where lines XP, YQ, and ZR intersect gives the center of gravity of the irregularly shaped wooden plank.

This text is adapted from Openstax, University Physics Volume 1, Section 12.2: Examples for Static Equilibrium.

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