The center of mass or center of gravity

is a point in an object in which its mass is concentrated. Each object (such as a ball, glass, ruler, or pigeon) can be thought of as a collection of mass points. When an object is supported at its center of mass, the mass is at equilibrium and (1) is balanced and (2) can rotate uniformly. The center of mass for a sphere is located at its center. If the sphere is supported at its center, the sphere would be able to be balanced and able to spin uniformly

However, the center of mass of objects can be counter intuitive to its geometric center. For example, a triangle’s center of mass is closer to its base. A race car is engineered to have more weight towards the bottom of the car so drivers can handle them during high speed turns. An object’s center of mass will always be towards its more massive end.

Center of Gravity[edit | edit source]

According to Newton’s law of universal gravitation, the earth exerts a force upon all objects on earth. This force is called gravity. The resultant force from an object’s mass and gravitational force is called its weight. This resultant goes through an object’s center of gravity. In a system containing the universal gravitation field, the weight of the object is concentrated at the center of gravity. The term center of gravity is used interchangeably with center of mass as long as the object experiences only earth's gravitational force

The center of gravity of a wrench on a parabolic path.

When an object is thrown in the air, its center of gravity would follow a parabolic path. The figure to the right shows a portion of a wrench at it is tossed into the air. The center of gravity of a wrench follows a path, even though other parts of the wrench do not. The center of gravity also moves equal distances in equal time intervals (because no force/acceleration is acting upon the wrench).

Locating the Center of Mass[edit | edit source]

Irregular Shaped Objects[edit | edit source]

Select any irregularly shaped object and suspend it from an edge on a string. Mark the plumb line, the line guided by the string, as reference.
Suspend the object from another location (not too close to the original location) and draw another plumb line. The intersection of the two plumb lines is the object’s center of mass. Note that the heart’s center of mass (C) is closer to the top because it’s more massive than the bottom.

Center of Mass Outside of Physical Structure of Object[edit | edit source]

The objects above have center of masses in mid-air.

The center of mass of an object may exist where there is no mass. A donut’s center of mass is at its center. This holds true for a hollow sphere such as a soccer ball. Even though the object’s mass is not concentrated at its center of gravity, when the object is tossed in the air, its center of gravity would follow a parabolic path. Other objects that have their center of gravity outside their physical structures include an empty pan or cup, a chair, or a boomerang.

Toppling[edit | edit source]

A box as it becomes toppled.

An object will topple once its plumb line falls outside of its base of support. The figure to the right shows a block being toppled over once its plumb line falls outside the base of the box

Applications[edit | edit source]

Keeping the Leaning Tower of Pisa from toppling has been a multinational task.

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Animal Tails[edit | edit source]

The horizontal distance to which an animal body can extend depends on how far it can keep its center of gravity within its base of support. A monkey can reach farther by extending its tail, keeping its center of gravity within the support of its feet. By extending its tail, it can shift its center of gravity to maintain balance and stability. Dinosaurs such as the Brachiosaurus had massive tails to help them keep their center of gravity above their feet so they can extend their heads.

Center of mass can make a soda can seem to defy gravity.

Trivia[edit | edit source]

  • The center of mass of a human body is at the pelvis area.
  • The center of mass of the solar system (when all planets are aligned collinearly) is about 2 solar radii from the sun’s center.
  • The center of mass of a rectangle is at the intersection of the two diagonals.
  • Alexander Calder, the inventor of mobiles, is famous for his sculptures that allow gusts of wind to arrange their elements. The structures of his mobiles are rearranged but the center of gravity always falls within the base of support (i.e. the pivot point).
  • Archimedes introduced the concept of center of gravity. He demonstrated that a single point on a lever is exerted the same amount of torque as weights resting at various points of the lever. He also developed methods to find centers of masses of regular shapes such as a triangle and hemisphere.

Brainteasers[edit | edit source]

  1. Boxes.jpg
    There are three trucks parked on a hill. The center of mass of each truck is marked with an “x”. Out of the three, which truck(s) would topple over?
  2. Bottle-and-Wood.jpg
    A bottle rack that seems to defy common sense is shown in the figure. Where is the center of gravity of the rack and bottle?

Solutions[edit | edit source]

  1. Only the first truck will topple over. Draw a plumb line from the center of mass of each truck to the ground. Only the first truck’s plumb line falls out of its base of support (i.e. the ground directly below the truck).
  2. The center of gravity is at point of the bottle directly above the base of support of the rack on the table. The center of gravity is over where the rack stands. It does not tip over because there is a a support beneath it.

See also[edit | edit source]

External links[edit | edit source]

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