# Gravity

## Gravitational Force

There is a gravitational force that acts between any two bodies that have mass, and the strength of this force is dependent upon how much mass each body has and the distance between the two bodies. The force of gravity is much greater between the Earth and a person then it is between two people because the Earth has a much larger mass than a person. No matter where an object is on the Earth, the force of gravity from the Earth always points from the object to the center of the Earth in a straight line.

For general purposes, when there is gravity, the center of gravity and the center of mass are the same thing. The center of gravity of a body is that point at which the force of gravity acts. The net effect of gravity is that it pulls on one point of the body, and that is the center of gravity. The center of gravity is where, if an object is supported at that spot, it will balance. For a symmetric object the center of gravity is located at the geometric center, like at the center of a square board. The center of mass of irregularly shaped objects is harder to find.

The center of mass of a flexible object is not stuck in one place in that object, and can also be located outside of the object. For example if a person is standing upright, their center of mass is located somewhere inside them near their waist. However, if the person puts on lots of heavy ankle weights then their center of mass will move down, towards their feet. Also, if the person bends over at the waist so their back is parallel to the floor then the center of mass will move outside the body. Another example of an object whose center of mass is located outside the body is a doughnut, where the center of mass is actually located in the hole.

## Center of Gravity

Walking on meter stick

• Arms out to side parallel to floor
Explanation: Holding your arms out to the side does not significantly affect the position of your center of gravity. However, by keeping both arms out to either side, your body is positioned symmetrically over the meter stick keeping the center of gravity over the meter stick. The reason it is easier to walk on the meter sticks in this position is really that you are increasing your rotational inertia. The tendency of a body to keep doing whatever it is doing, staying still or rotating for example, is called inertia. If an objectâ€™s inertia is increased then it is harder to create any change in its motion. Inertia can be increased by adding more mass farther from the axis of rotation, or by redistributing the existing mass farther out. By holding your arms out to the side, you are increasing your inertia by moving your weight away from the axis of rotation (the meter stick) and therefore making it harder to move you from the balanced position over the meter stick. That is why it is easier to walk on the meter stick in this position.
• Arms crossed over chest
Explanation: Similar the position described above, this position is harder not because the center of gravity has been moved, but because the inertia has been decreased. By crossing your arms over your chest, all of your mass (and therefore your center of mass) is centered directly over the meter stick. So, because the inertia is decreased it is easier for any slight deviation from the vertical to cause the center of gravity to move out from over the meter stick, making you fall off. That is why it is harder to walk on the meter stick in this position.
• Holding book in one hand out to side, the other arm down.
Explanation: By holding a book in one hand out to the side, you are moving your center of gravity to that side. Because the other arm is not out, but down by your side, there is no weight to counter balance the book (as in part (a) where both arms were out). If the book is heavy enough or held far enough away from your body, then the combined center of mass of you and the book can move out to the side far enough so that it is no longer over the meter stick, making you fall off. In order to keep you from falling off, the common response is to extend the other arm and bend to the side opposite from the books. Both of these motions change the configuration of the mass, pulling the center of gravity back over the meter stick. That is why it is hard to walk on the meter stick in this position.
• Holding book with both hands below waist
Explanation: When the book is held with both hands below your waist, you are lowering the combined center of gravity of you and the book and positioning it closer to the meter stick. Although walking in this position is easier than walking with the book out to the side, it is not the most secure way to balance over the meter stick. However, the reason it is more stable is because lowering the position of the center of gravity reduces the moment arm (the distance from the meter stick to the center of gravity), hence reducing the gravitational torque (the force that would cause you to rotate to the side and fall off the stick) that is trying to topple you if your center of mass momentarily is not over the meter stick.

Balancing clown