An object on a point that rotate a fixed axis has circular motion around the same axis. Linear quantities cannot be used for circular motion. This is due to the extended objects rotational motion rather that a particles linear motion. Circular motion, for this reason, is described in terms of the change in angular position. Except for the points on the axis, all the points on a rotating rigid object during any time interval move through the same angle.
Many equations describing circular motion require angles to be measured in radians (rad) instead of degrees. Any angle θ measured in radians, in general, is defined by the equation. If the arc length, s, and the length of the radius, r, is equal, the angle θ swept by r is equal to one radian. The units cancel and the abbreviation radian is substituted because θ is the ratio of the length of the radius (distance) to an arc length (also a distance). In other words, the radian is a pure number, with no dimensions.
When the light on a Ferris wheel moves one revolution of the wheel (angle of 360˚) the circumference of a circle, which is r, is equal to the arc length s. By substituting this value for s (into the equation above) gives the corresponding angle in radians . Hence radians equals 360˚, or one complete revolution. An angle approximately 2(3.14) =6.28 radians corresponds with one revolution. Figure 1 to the right is a circle that is marked with both degrees and radians.
Any angle that is in degrees can be converted into radians by multiplying the degree with . With this method, the degree would cross out leaving the measurements in radians. The conversion can be simplified as . Angular displacement is the change in the arc length, Δs, divided by the distance of the bulb from the axis of rotation. The equation of angular displacement is a. This equation and the equation for linear displacement are similar because the equations denotes a change in position. However, the difference is...
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