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Question Number 5718 by Rasheed Soomro last updated on 25/May/16

$$\mathrm{Two}\mathrm{angles}\mathrm{can}\mathrm{be}\mathrm{added}\mathrm{and}\mathrm{subtracted}.$$$$\mathrm{Can}\mathrm{we}\mathrm{multiply}\mathrm{them}\mathrm{also}?$$$$\mathrm{For}\mathrm{example}$$$$\mathrm{x}\mathrm{radians}\times \mathrm{y}\mathrm{radians}=\mathrm{xy}{\left(\mathrm{radians}\right)}^2?$$$$\mathrm{What}\mathrm{will}\mathrm{be}\mathrm{the}\mathrm{meaning}\mathrm{of}{\left(\mathrm{radians}\right)}^2$$$$\left(\mathrm{square}\mathrm{radians}\right)?$$

Commented by FilupSmith last updated on 25/May/16

$$\theta =\mathrm{angle}\mathrm{in}\mathrm{radians}$$$$\theta \in (0,2\pi ]$$$$\therefore 0⩽\theta <2\pi$$$$$$$$\mathrm{if}\theta ⩾2\pi :\theta =2\pi +k$$$$\mathrm{then}\theta =k\left(\mathrm{in}\mathrm{most}\mathrm{situations}\right)$$$$$$$$\mathrm{although}\mathrm{I}\mathrm{am}\mathrm{unsure}\mathrm{about}\mathrm{your}\mathrm{question},$$$$\mathrm{I}\mathrm{would}\mathrm{assume}\mathrm{that}\mathrm{you}\mathrm{can}\mathrm{multiply}.$$$$$$$$\mathrm{e}.\mathrm{g}.$$$$\theta =ab\left(a\mathrm{and}b\mathrm{and}\mathrm{angles}\right)$$$$\mathrm{if}ab=2\pi +k,k⩾0$$$$ab=k$$$$\therefore \theta =k$$$$$$$$\mathrm{sorry}\mathrm{about}\mathrm{the}\mathrm{bad}\mathrm{answer}.$$

Commented by prakash jain last updated on 25/May/16

$$\mathrm{Centripetal}\mathrm{accelaration}={\omega }^{2}r$$$$\mathrm{So}\mathrm{there}\mathrm{is}\mathrm{multiplication}\mathrm{of}\mathrm{angular}\mathrm{component}.$$$$\mathrm{However}\mathrm{radian}\mathrm{is}\mathrm{a}\mathrm{dimensionless}$$$$\mathrm{quantity}\theta =\frac{\mathrm{arc}\mathrm{length}}{\mathrm{radius}}$$

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