A particle is moving uniformly in a circular path of radius r . When it moves through an angular displacement θ , then the magnitude of the corresponding linear displacement will be

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ln Δ A OB sin 2 θ ​ = A O A B ​ ⇔ A O = r ) A B A C A C ​ = A O sin 2 θ ​ ⇒ A B = r sin 2 θ ​ = A B + BC ( ∵ A B = BC ) = r sin 2 θ ​ + r sin 2 θ ​ = 2 r sin 2 θ ​ ​ So, the magnitude of the corresponding linear displacement will be 2 r sin 2 θ ​

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