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Kinds of Magnetic Materials

instantaneous velocity, scalar quantity, centripetal acceleration, air friction, magnitude of velocity

Kinetics is the description of motion without regard to what causes the motion. Velocity (the time rate of change of position) is defined as the distance traveled divided by the time interval. Velocity may be measured in such units as kilometers per hour, miles per hour, or meters per second. Acceleration is defined as the time rate of change of velocity: the change of velocity divided by the time interval during the change. Acceleration may be measured in such units as meters per second per second or feet per second per second. Regarding the size or weight of the moving object, no mathematical problems are presented if the object is very small compared with the distances involved. If the object is large, it contains one point, called the center of mass, the motion of which can be described as characteristic of the whole object. If the object is rotating, it is frequently convenient to describe its rotation about an axis that goes through the center of mass.

To fully describe the motion of an object, the direction of the displacement must be given. Velocity, for example, has both magnitude (a scalar quantity measured, for example, in meters per second) and direction (measured, for example, in degrees of arc from a reference point). The magnitude of velocity is called speed.

Several special types of motion are easily described. First, velocity may be constant. In the simplest case, the velocity might be zero; position would not change during the time interval. With constant velocity, the average velocity is equal to the velocity at any particular time. If time, t, is measured with a clock starting at t = 0, then the distance, d, traveled at constant velocity, v, is equal to the product of velocity and time. d = vt

In the second special type of motion, acceleration is constant. Because the velocity is changing, instantaneous velocity, or the velocity at a given instant, must be defined. For constant acceleration, a, starting with zero velocity ( v = 0) at t = 0, the instantaneous velocity at time, t, is v = at. The distance traveled during this time is d = 1/2at2. An important feature revealed in this equation is the dependence of distance on the square of the time (t2, or t squared, is the short way of notating t x t). A heavy object falling freely (uninfluenced by air friction) near the surface of the earth undergoes constant acceleration. In this case the acceleration is 9.8 m/sec/sec (32 ft/sec/sec). At the end of the first second, a ball would have fallen 4.9 m (16 ft) and would have a speed of 9.8 m/sec (32 ft/sec). At the end of the second second, the ball would have fallen 19.6 m (64 ft) and would have a speed of 19.6 m/sec (64 ft/sec).

Circular motion is another simple type of motion. If an object has constant speed but an acceleration always at right angles to its velocity, it will travel in a circle. The required acceleration is directed toward the center of the circle and is called centripetal acceleration (see Centripetal Force). For an object traveling at speed, v, in a circle of radius, r, the centripetal acceleration is

Another simple type of motion that is frequently observed occurs when a ball is thrown at an angle into the air. Because of gravitation, the ball undergoes a constant downward acceleration that first slows its original upward speed and then increases its downward speed as it falls back to earth. Meanwhile the horizontal component of the original velocity remains constant (ignoring air resistance), making the ball travel at a constant speed in the horizontal direction until it hits the earth. The vertical and horizontal components of the motion are independent, and they can be analyzed separately. The resulting path of the ball is in the shape of a parabola.

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