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Question

Obtain the relation between linear velocity and angular velocity

Solution
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Consider a particle moving with uniform circular motion in anticlock wise direction with centre O and radius r the particle cover an arc of length s in time t moving from A to B.
Hence the angular displacement is
θ=sr
Dividing both side by t
θt=1rst
In the time interval t be infinitesimally small (t0), then
limtθθt=1r[limtθst]
But limtθθt=ω and limtθst=V
ω=Vr
V=rω
In vector form, V=ω×r
629087_601484_ans_1f9a63519c2e459fbd73f734cfa83111.png

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