A thin rod of mass $$0.9$$ kg and length $$1$$ m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of mass $$0.1$$ kg moving in a straight line with velocity $$80$$ $$m/s$$ hits the rod at its bottom most point and sticks to it (see$$ $$figure). The angular speed (in$$ $$rad/s) of the rod immediately after the collision will $$be____$$

Question

Infinity Learn · Accepted Answer

Applying conservation of angular momentum of particle $$+$$ rod about the $$hingeLi=Lf$$​⇒muL $$+Irodwinitial=Iparticle+Irod$$ωfinal​⇒m×u×$$L+0=mR2+MR23$$ω​⇒$$1$$×$$0.1$$×$$80+0=0.1$$×$$12+0.9$$×$$123$$ω​⇒$$8=0.4$$ω​⇒ω$$=20$$ $$rad/s$$

Rotational motion

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Rotational motion

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Applying conservation of angular momentum of particle + rod about the hingeLi=Lf​⇒muL +Irodwinitial=Iparticle+Irodωfinal​⇒m×u×L+0=mR2+MR23ω​⇒1×0.1×80+0=0.1×12+0.9×123ω​⇒8=0.4ω​⇒ω=20 rad/s

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