![]() Or we might say the earth rotates at at 0.00007272 (7.272 x 10 -5 ) rad/s counterclockwise relative to the sun as viewed from above the north geographic pole this tells us the earth's angular velocity. We might say the earth rotates at at 7.272 x 10 -5 rad/s, and this tells us its angular speed. Angular speed is a Scalar (dimensionless) quantity, while angular velocity is a vector quantity consisting of angular speed and direction in the form of a rotational sense (clockwise or counterclockwise). It is important to realize that angular speed is not the same thing as angular velocity. ![]() This is a theoretical value, because it cannot be obtained except by inference from measurements made over progressively shorter time spans. The instantaneous angular speed, u inst, is the limit of the measured average speed as x approaches zero. Where the added and subtracted numbers represent seconds. The average angular speed can be measured over increasingly short time intervals centered at p, for example: ![]() Suppose an object is in rotational motion at about that time. Let p represent a specific point in time. Instantaneous angular speed is more difficult to intuit, because it involves an expression of motion over an "infinitely short" interval of time. If u avg represents the average angular speed of an object (in radians per second) during a time interval t (in seconds), and the angle through which the object rotates in that time is equal to q (in radians), then: This quantity can be defined in either of two senses: average or instantaneous.Īverage angular speed is obtained by measuring the angle in radian s through which an object rotates in a certain number of seconds, and then dividing the total angle by the time. The radian per second (symbolized rad/s or rad/sec) is the Standard International ( SI ) unit of angular (rotational) speed.
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