A conical pendulum consists of a bob of mass m in motion in a circular path in a horizontal plane as shown in figure. During the motion, the supporting wire of length l, maintains a constant angle θ with the vertical. The magnitude of the angular mornentum of the bob about the vertical dashed line is

Question

A conical pendulum consists of a bob of mass m in motion in a circular path in a horizontal plane as shown in figure. During the motion, the supporting wire of length l, maintains a constant angle θ with the vertical. The magnitude of the angular mornentum of the bob about the vertical dashed line is

Infinity Learn · Accepted Answer

We start with the particle under a net force model in the x and y directions:∑ Fx $$=$$ max :T $$sin$$ θ $$=$$ $$mv2r$$∑ Fy $$=$$ may : T $$cos$$ θ $$=$$ mgSo $$sin$$ θ$$cos$$ θ $$=$$ $$v2rg$$ and v $$=$$ rgsin θ$$cos$$ θthen L $$=$$ rmv $$sin$$ $$900$$ $$=$$ rmrgsin θ$$cos$$ θ $$=$$ $$m2gr3sin$$ θ$$cos$$ θand since r $$=$$ l $$sin$$ θ,L $$=$$ $$m2gl3sin4$$θ$$cos$$ θ

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