Reference: Beginning Physics I
CHAPTER 4: FORCES IN EQUILIBRIUM
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KEY WORD LIST
Force, Resultant Force, Line of Action, Rigid Body, Translational Motion, Center of Mass, Uniform Translational Motion, Rotational Motion, Translational Equilibrium, Rotational Equilibrium, Frame of Reference, Inertial Frame of Reference, Newton’s First Law, Law of Equilibrium, Collinear Forces, Concurrent Forces, Body Diagram, Newton’s Third Law, Friction, Normal Force, Static Friction, Kinetic Friction
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GLOSSARY
For details on the following concepts, please consult CHAPTER 4.
FORCE
A force is a mechanical effect of the environment on an object. It is either a push or a pull that manifests either as motion or as distortion of the object. Force may be applied through direct contact or from a distance, such as, the magnetic force. Mathematically, a force can be represented by a vector as it has both a magnitude and a direction. Coplanar forces are “forces” that are acting in the same plane.
RESULTANT FORCE
The vector sum of the forces acting on a particle is called the resultant force on that particle. The forces acting on a particle may be replaced by their resultant, and it will have the same effect.
LINE OF ACTION
The line of action of a force is an imaginary line parallel to the force and drawn through the point at which the force is acting. A force acting on a rigid body can be applied anywhere along its line of action and still have exactly the same effect.
RIGID BODY
A rigid body refers to an object that doesn’t change its shape when forces act on it. No real object is truly rigid, but the concept is a good approximation for stiff objects
TRANSLATIONAL MOTION
Translational motion is the motion of an object as a whole, through space, without regard to how it spins on itself. The translational motion of a very small object, idealized as a particle, is just the motion of the particle along its path.
CENTER OF MASS
The center of mass is a special point of an object, whose translational motion represents the translational motion of the object as a whole, through space, without regard to how it spins on itself. For simple uniform symmetric objects, such as a disk, a sphere, a rod, or a rectangular solid, the center of mass is at the geometric center of the object.
UNIFORM TRANSLATIONAL MOTION
Uniform translational motion means that the center of mass of the object is either at rest or moving at constant speed in a straight line.
ROTATIONAL MOTION
Rotational motion is the spinning motion of an object about a fixed axis, such as the spinning of a wheel on a shaft, but it can also refer to the spinning of an object on itself as the object moves through space. Rotational motion is the change in the angular orientation of the object.
TRANSLATIONAL EQUILIBRIUM
Translational equilibrium means that the object as a whole, aside from rotation, has uniform translational motion. This is the case when the forces acting on an object add up to zero.
ROTATIONAL EQUILIBRIUM
Rotational equilibrium means that the object—whether it is undergoing translational motion or not—is either not spinning or it is spinning in a uniform fashion. For simple symmetric objects it means spinning at a constant rate about a fixed direction.
FRAME OF REFERENCE
A Frame of Reference refers to the “framework” that defines the coordinate system in which one’s measurements and observations are made. If a coordinate system is fixed to the earth and another one is fixed to a rotating merry-go-round, one is going to observe things differently in each. Each of these coordinate systems is fixed in a different frame of reference.
INERTIAL FRAME OF REFERENCE
An inertial frame of reference is a frame of reference in which a completely isolated object (no forces) will appear to be in both translational and rotational equilibrium. For most purposes the earth can be considered an inertial frame. The importance of inertial frame is that Newton’s laws hold only in such frames, and most of the other laws of physics take on simpler form when described in such frames.
NEWTON’S FIRST LAW
Newton’s first law is the condition that the center of mass of the object is either at rest or moving at constant speed in a straight line. Here the vector sum of all forces acting on the object is zero.
LAW OF EQUILIBRIUM
See Newton’s first law.
COLLINEAR FORCES
Two forces are collinear when they act along a common line of action.
CONCURRENT FORCES
Three forces are concurrent when their lines of action pass through a common point.
BODY DIAGRAM
Body diagram, as drawn, consists of the isolated object with only the forces acting on it.
NEWTON’S THIRD LAW
This law, otherwise known as the law of action and reaction, states that if some object exerts a force on another object, then the other object exerts a force back that is equal in magnitude and opposite in direction. The law holds both for contact forces and for action-at-a-distance forces.
FRICTION
Friction is the rubbing force between two objects whose surfaces are in contact. The force of friction always acts parallel to the touching surfaces. The magnitude of the frictional force exerted by each surface on the other depends on how tightly the two surfaces are pressed together.
NORMAL FORCE
The force responsible for two surfaces pressing together is called the normal force because it acts perpendicular to the two surfaces. By Newton’s third law each surface exerts a normal force that is equal in magnitude and opposite in direction to that exerted by the other.
STATIC FRICTION
When two surfaces are at rest with respect to one another, the frictional force each exerts on the other always opposes any tendency to relative motion. The frictional force on an object adjusts itself in magnitude and direction to oppose and counterbalance any other forces on the object that would tend to make the object start to slide, as needed, from zero magnitude up to some maximum value to stop such slippage. The maximum static friction force that one surface can exert on another is proportional to the normal force, and the proportionality constant is called the coefficient of static friction. This coefficient depends on the nature of the two surfaces.
KINETIC FRICTION
Once two surfaces are in motion relative to one another, the frictional force, now called kinetic friction, acting on a surface is always in a direction opposed to the velocity of that surface. Its magnitude is independent of the magnitude of the velocity. The coefficient of kinetic friction is equal to or smaller than the coefficient of static friction for any given pair of surfaces.
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