Easyphysics: Units of Angular Displacement

Wednesday, 25 May 2011

Units of Angular Displacement

Three units are generally used to express angular displacement, namely degrees, revolution and radian. We are familiar with the first two. As regards radian which is SI unit, consider an arc of length S of a circle of radius r which subtends an angle Ѳ at that center of the circle given in radians (rad) as shown in the figure given below:

$\dpi{80} \fn_jvn \theta =\frac{arc\; length}{radius}\; \; \; rad$

$\dpi{100} \fn_jvn \theta =\frac{s}{r}\; \; \; rad$

Or

$\dpi{100} \fn_jvn s = r\;\theta$

If OP is rotating, the point P covers a distance

in one revolution of P. In radian it would be,

$\dpi{100} \fn_jvn \frac{s}{r}=\frac{2\pi r}{r}=2\pi$

1 revolution = $\dpi{100} \fn_jvn 2\pi\;\; rad=360^{\circ}$

$\dpi{100} \fn_jvn 1 \; rad =\frac{360^{\circ}}{2\pi }=57.3^{\circ}$

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