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Obtain the relation between angular velocity and linear velocity.

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Consider a particle moving in a circle of radius ‘r’ with uniform angular velocity ‘ ω ’ and linear speed ‘V’. Let the particle moves from A to B in time ‘t’ seconds through a small distance ‘s’ on the circumference. Let θ be the angular displacement.

Angular velocity ω = \(\frac{\theta}{\tau} \)

Angular displacement \(\)θ = \(\frac{s}{\tau}\)

∴ ω = \(\frac{s}{\tau_{r}}\)

But \(\frac {s} {s}\)= v, linear velocity

∴ ω = \(\frac{v}{r} \,or\)

v = r ω

linear velocity = radius × angular velocity.

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