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Texts Kinematics

2.5.1 Read the text and answer: What is motion, plane motion, rotation, plane of rotation, center of rotation, S-coordinate,uniform motion,nonuniform motion, angular displacement?

Motion. — The commonest phenomena which we observe are those involving the movement of objects from one point to another. Walking, riding, flying, dancing, climbing and sailing are all familiar examples of motion.

Motion is the continuous change in position of an object or a par­ticle. The line along which a moving particle travels is called the path of the particle or path of the motion. If the path is a straight line the motion is rectilinear; if it is a curved line the motion is curvilinear.

Plane Motion is motion in which each point of the moving body remains at a constant distance from a fixed plane. Each point of the body moves in a plane, and that plane in which the center of gravity of the body moves is called the plane of the motion.

The wheels of a locomotive running on a straight track have plane motion, as has also a book which is slid about in any way on the top of a table. A translation may or may not be a plane motion; a ro­tation about a fixed axis is always a plane motion.

A rotation is such a motion of a rigid body that one line of the body or of an extension of the body remains fixed. The fixed line is the axis of rotation. The motion of the flywheel of a stationary engine is rotation, and the axis of rotation is the axis of the shaft on which the wheel is mounted; the motion of an ordinary clock pendulum is a rotation, and the axis of rotation is the horizontal line through the point of support and perpendicular to the pendulum. Obviously all par­ticles of a rotating body except those on the axis describe circles or circular arcs whose centers are in the axis and whose planes are per­pendicular to the axis. The plane in which the center of gravity of the body moves is the plane of rotation and the intersection of the axis of rotation and this plane is the center of rotation. All particles of the body on any line parallel to the axis move alike, hence the motion of the projection of the line on the plane of rotation represents the motion of all these particles. And the motion of the body itself is represented by the motion of the projection of the body on the plane of rotation.

Position; Displacement. — The position, at any instant, of a particle that has rectilinear motion is conveniently specified by its distance from a chosen fixed origin in the path. We call this distance the S-coordinate and customarily denote it by S. To indicate which side of the origin the moving particle is on, S is given a sign. Either direction along the path may be taken as positive and the other as negative. We assume for convenience that rectilinear motions are hori­zontal, and we take direction to the right as positive. The displacement of a particle for any given interval of time is the increment in its S-coordinate; it is equal to the distance between the initial and final positions of the particle, and is positive when the final position is to the right of the initial position.

If the direction of the motion does not change during a given in­terval of time, the displacement of the particle for that interval is equal to the distance it travels. But if the motion is reversed during the interval the distance travelled is greater than the displacement. If a particle moves so that it undergoes equal displace­ment in all equal intervals of time it has uniform motion; if it moves in any other way it has nonuniform motion.

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