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A particle is moving with constant speed u along line y = a in positive X direction find magnitude of its angular velocity Omega about origin when its position vector makes an angle theta with positive x-axis
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Asked by jhajuhi19 | 18 May, 2019, 20:43: PM
answered-by-expert Expert Answer
as the particle P moves in the line y = a with constant speed v,  angle θ made by line OP with axis is given by, 
 
tanθ = a/(vt)  .............................(1)
 
By differentiating eqn.(1),  sec2θ (dθ/dt) = -(a/v) (1/t2 ) = -(a/v) (v2 / a2 ) tan2θ  .....................(2)
 
In eqn.(2), (1/t) is substituted as (v/a)tanθ  using eqn.(1)
 
after simplification, we get from eqn.(2),  angular velocity ω = (dθ/dt) = - (v/a) sin2θ
Answered by Thiyagarajan K | 18 May, 2019, 22:24: PM

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