Center of Mass

• M.3(1) - Leaning Tower of Pisa
• M.3(2) - Double Cone and Inclined Plane
• M.3(3) - Center of Mass Apparatus
• M.3(4) - Finding the Center of Gravity
• M.3(5) - Pendulum on the Cart
• M.3(6) - Center of Gravity Paradox
• M.3(7) - The Feeble Minded Disc
• M.3(8) - The Plastic Bird

M.3(1) - Leaning Tower of Pisa

This 25 cm high wooden "tower" shows the effects of changing an object's center of mass. The "tower" is stable when the center of mass is above the base, ie, the "tower" without the top. When the top is in place, it tumbles over.

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M.3(2) - Double Cone and Inclined Plane

A double cone apparently rolls uphill freely whereas a uniform cylinder rolls the other way. The demonstration emphasizes the apparent motion in contrast to that of the center of gravity of the cone.

The inclined plane is formed by V-shaped wood bars, as in the figure. Place the cylinder at the top end of the inclined place. The cylinder naturally rolls downward. Now locate the double cone symmetrically at the bottom (narrow end) of the inclined plane. It rolls upward: as the wood bars diverge, the axis of the double cone is actually moving down.

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M.3(3) - Center of Mass Apparatus

This apparatus consists of 2 different size balls connected by a bar. The bar can be made to spin smoothly about the apparatus' center of mass but not about the apparatus' geometrical center. The bar is about 20 cm long and the balls are 1 cm and 2 cm in diameter. The second set has a 45 cm bar and the balls are 2 cm and 7 cm in diameter.

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M.3(4) - Finding the Center of Gravity

The center of gravity of any body can be found by suspending it from one pivot point and then another, and another. The lines drawn along the string supporting a plumb will all cross at a common point: the center of gravity.

The same procedure is also available with the Blackboard Mechanics Set (see M.1)

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M.3(5) - Pendulum on the Cart

It shows that the center of mass remains at constant velocity.

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M.3(6) - Center of Gravity Paradox

This simple apparatus consists of a 1.2 m metal rod and a lead slide weight secured with a thumb screw. It is used to show that a position of higher center of gravity is easier to balance because the system is slower to react to unbalanced forces. First balance the rod with the load near the finger tip. It is clearly very difficult to do so. Now turn the rod over and balance it. With the center of gravity much higher it does not tip over so easily

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M.3(7) - The Feeble Minded Disc

The apparatus is an approximately 25 cm diameter hardwood disk. When it is placed on an inclined plane, it rolls up the plane! When it is placed on the lecture table it promptly rolls to the edge and stops! Its center of mass can be determined by suspending it successively by the holes located around its periphery. It shows that the the stable position of a body is that for which the center of mass is at the lowest possible elevation.

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M.3(8) - The Plastic Bird

Use this small piece of plexiglass and a belt to do an interesting demonstration on center of mass. It shows that the stability of equilibrium of a hanging body depends on the position of the center of gravity with respect to the point of support.

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