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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
Asked by jhajuhi19 | 18 May, 2019, 08:43: PM
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, 10:24: PM
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