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Rotation Concept

A particle mo...

Question

A particle moves on a given straight line with a constant speed $v$ . At a certain time it is at a point $P$ on its straight line path. $O$ is a fixed point. Show that $\to O P \times \to v$ is independent of the position $P$ .

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Solution

Consider the particle moves on the straight line $P P$ ' at speed $v$ .

OP x v = (OP) v sinФ n = v(OP) sinФ n = v(OQ) n

So,

$O Q = O P s i n Ф = O P^{'} s i n Ф$

So, the magnitude of $O P x v$ remain constant irrespective of the position of the particle.

Hence , OP x v is independent of position $P$ .

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