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A small particle of mass on is projected with an initial velocity v at an angle 8 with x axis in X-Y plane as shown in Figure. Find the angular momentum of the particle.

Answer» <html><body><p></p>Solution :Let the particle of mass m cross a horizontal distance x in time t. <br/> <a href="https://interviewquestions.tuteehub.com/tag/angular-11524" style="font-weight:bold;" target="_blank" title="Click to know more about ANGULAR">ANGULAR</a> momentum `vecL= int vec <a href="https://interviewquestions.tuteehub.com/tag/tau-663951" style="font-weight:bold;" target="_blank" title="Click to know more about TAU">TAU</a> dt` <br/>But `vectau= vecr xx vec F` <br/> `vecr=xhati+yhatj and vecF=-mg hatj` <br/> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/FM_PHY_XI_V01_C05_SLV_028_S01.png" width="80%"/> <br/> `:. Tau=(x hati+y hatj)xx(hati xx hatj)=-mgx hatk` <br/> `vecL=-mg int (x dt) hatk=- mgv cos theta( intdt) hatk)` <br/> Let <a href="https://interviewquestions.tuteehub.com/tag/initial-499269" style="font-weight:bold;" target="_blank" title="Click to know more about INITIAL">INITIAL</a> time =0 and final time `t=t_(1)` <br/> `:. vecL= mgv cos theta( underset(0) <a href="https://interviewquestions.tuteehub.com/tag/overset-2905731" style="font-weight:bold;" target="_blank" title="Click to know more about OVERSET">OVERSET</a>(t_(f)) int t dt) hatk=-(1)/(2) mgv cos theta t_(f)^(2) hatk` <br/> Negative <a href="https://interviewquestions.tuteehub.com/tag/sign-1207134" style="font-weight:bold;" target="_blank" title="Click to know more about SIGN">SIGN</a> indicates, `vecL` point inwards</body></html>


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