Physics I: Chapter 9

Reference: Beginning Physics I

 CHAPTER 9: RIGID BODIES I: EQUILIBRIUM & CENTER OF GRAVITY

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KEY WORD LIST

Equilibrium, Torque, Moment, Laws of Equilibrium (Rigid Bodies), Equivalent Sets of Coplanar Forces, Center of Gravity, Couple

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GLOSSARY

For details on the following concepts, please consult CHAPTER 9.

EQUILIBRIUM
For introduction to translational and rotational equilibrium. See Chapter 4.

For a situation in which every slight tilt from equilibrium gives rise to a couple that restores equilibrium, we say that the equilibrium is stable.

Whenever a slight tilt of an object away from equilibrium gives rise to a couple that continues the motion away from equilibrium, we say the equilibrium is unstable.

TORQUE
The words torque and moment are synonymous. They are used interchangeably in the present context.

MOMENT
The moment of a force is a tendency to produce motion about an axis. It is the product of a force and its directed distance from an axis. The axis is selected as a point in the plane of the force, and rigidly linked to the body. A moment arm is defined as the perpendicular distance from this point to the line of action of the force. The moment of the force is defined as the product of the magnitude of the force and length of the moment arm.

The plus sign indicates that the force would tend to rotate the body counterclockwise about the point chosen as the axis. The negative sign indicates clockwise rotation.

LAWS OF EQUILIBRIUM (RIGID BODIES)
The following are the necessary and sufficient conditions for translational and rotational equilibrium for a rigid body acted on by any number of coplanar forces:

  1. The vector sum of the forces must vanish.
  2. The algebraic sum of the torques about a given point must vanish.

Mathematically,

EQUIVALENT SETS OF COPLANAR FORCES
One can always replace one set of forces acting on a rigid body by any other set of forces having the same vector sum and the same resultant torque (about any chosen point) to get the same effect on the motion of the body.

CENTER OF GRAVITY
The center of gravity is the point in the body where the total weight can be assumed to be acting. The center of gravity and the center of mass are one and the same point.

COUPLE
A couple is a pair of equal and opposite forces giving rise to a torque.

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