Center of Gravity

Unit 6

Center of gravity- the point on an object located at the object’s average position of weight

Symmetrical object (baseball)- CG is at the geometric center

Irregularly shaped object (baseball bat)- CG is towards the heavier end

Objects not made of the same material throughout may have the center of gravity quite far from the

geometric center.

If a wrench were slid along a straight path, the CG follows a straight-line path. Other parts of the wrench rotate about this point as the wrench moves across the surface.

Center of gravity is often called center of mass, which is the average position of all particles of mass that

make up an object.

Measuring center of gravity

The CG of a uniform object (such as a meter stick) is at the midpoint, its geometric center. The CG is the balance point. Supporting that single point supports the whole object.

Measuring center of gravity

If you suspend any object (for ex, a pendulum) at single point, the CG of the object will hang directly below the point of suspension. To locate the CG, construct a vertical line beneath the point. The CG lies somewhere along that line. You can locate the CG by suspending the object from some other point and constructing a second vertical line. The CG is where the two lines intersect.

The CG of an object may be located where no actual material exists (for example, a ring’s CG is the hollow

center).

Look at the picture below. You can see that the block will begin to topple when the plumb line extends beyond the supporting base of the block. The rule is this: if the CG is

above the area of support, the object will remain upright. If the CG extends outside the area of support, the object will

topple.

This explains why the Leaning Tower of Pisa does not topple; its CG does not extend beyond its base.

Consider a solid wooden cone on a level table. You cannot stand it on its tip. Even if you position it so that its

CG is exactly above its tip, the slightest vibration will cause the cone

to topple.

However, a cone balances easily on its base.

An object balanced so that any displacement lowers its CG is in unstable equilibrium.

An object that is balanced so that any displacement raises its CG is in stable equilibrium.

An object placed in a position where the CG is neither raised nor lowered is in neutral equilibrium.

The CG of a building is lowered if most of the structure is below ground

level. This structure is so deeply “rooted” that its CG is actually below ground level making it very stable.

When you stand erect with your arms hanging at your sides, your CG is within your body. It is typically 2 to 3 cm below your navel, and midway between your

front and back. The CG is slightly lower in women than in men because women tend

to be proportionally larger in the pelvis and smaller in the shoulders. In children,

the CG is approximately 5% higher because of the proportionally larger heads

and shorter legs.

When you stand, your CG is somewhere above your support

base, the area bounded by your feet. In unstable situations, as in standing

in the aisle of a bumpy-riding bus, you place your feet farther apart to

increase this area.