• The center of gravity of an object is the point through which the entire weight of the object appears to act.

The center of mass is the mean position of the mass in an object.

Then there's the center of gravity, which is the point

where gravity appears to act. But they're only the same when

the gravitational field is uniform across an object.

Locating the Center of Gravity• The center of gravity of a

uniform object is at the midpoint, its geometric center.

Locating the Center of Gravity• When the

distribution of mass of the object is not constant or the object is not uniform the center of gravity shifts to the direction of greater mass.

Locating the Center of Gravity• The CoG of an object may be located where no actual material exists.

Locating the Center of GravityRest a meter stick on two extended forefingers. Slowly bring your fingers together. Note what occurs as your fingers meet at the CoG. When one finger gets ahead of the other, weight on it increases, enough to keep it from moving, while the other finger, with less friction, slides and catches up. You end up at 50 cm mark because the fingers always meet at CoG!

Locating the Center of Gravity• When you stand straight

with your arms hanging at your sides, your CoG is within your body. It is typically 2 to 3 cm below your navel and midway between your front and back.

Locating the Center of Gravity• The CoG is slightly lower in women than in men because women tend to be proportionally larger in the pelvis and smaller in the shoulders.

Locating the Center of Gravity• In children, the CoG is slightly 5% higher because of their proportionally larger heads and short legs.

Comparison of Factors Affecting Location of Center of Gravity in the Human Body

Relative to Age and Gender

Comparison of Factors Affecting Location of Center of Gravity in the Human Body

Relative to Load being Carried

Location of center of gravity shifts whenever the person shifts

position.

Positions where center of gravity is outside the body.

Toppling• If the CoG of an object is above the area of support, the object will remain upright. If the CG extends outside the area of support, the object will topple over.

The Leaning Tower of Pisa does not topple over because its CG does not extend beyond its base! And so the tower has stood for centuries.

• When you carry a heavy load –such as a pail of water-with one arm, why do you tend to hold your free arm out horizontally?

Toppling

You tend to hold your free arm outstretched to shift the CoG of your body away from the load so your combined CoG will more easily be above the base of support.

• To resist being toppled, why does a wrestler stand with feet wide apart and bent knees?

Toppling

A wide apart feet increase the support base. Bent knees lower the CoG.

Toppling• What is the importance of tails of an animal in terms of toppling?

Tail gives an animal the ability to shift its CoG and increase stability

Stability

Racing cars have really low centres of gravity so that they can corner rapidly without turning over.

• The position of the center of gravity of an object affects its stability. • The lower the center of gravity (CoG) is, the more stable the object.

Stability• Increasing the area of the base will also increase the stability of an object, the bigger the area the more stable the object.

Stability• Figure 4 shows a car tilting at ever increasing angles until eventually it will topple! 

Stability• The effect of size of the base is shown by the three stools in Figure 5. The center of gravity of all the stools are the same height above the ground but because stool (c) has a much smaller base it topples over if they are all tilted to the same angle while the other two stools return to a level position. Notice that the centre of gravity is not inside the material of the stool.

Stability• The pictures in Figure 7 show why it is not a good idea to stand up and then lean over in a small boat. The high center of gravity of the standing people makes it all too easy to tip the boat over! 

Stability & Equilibrium• Equilibrium is UNSTABLE when the CoG is lowered with displacement, STABLE when work must be done to raise the CoG and NEUTRAL when displacement neither raises nor lowers the CoG.

• A cone balances easily on its base. To make it topple, its CoG must be raised. This means the cone’s potential energy must be increased, which requires work.

Stability & Equilibrium

• If you position the cone so that its CoG is exactly above its tip, the slightest vibration or air current will cause the cone to topple. The CoG is lowered by any movement.

Stability & Equilibrium

• When the cone is placed on its side its CoG is neither raised nor lowered with displacement.

Stability & Equilibrium

Stability & EquilibriumStable – the center of gravity is raised as it is tiltedUnstable – the center of gravity is lowered as it is tiltedNeutral - the center of gravity stays at the same level if it is pushed