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Angular momentum of a projectile

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Today we look at an interesting problem that helps us feel closely the concept of angular momentum of a moving point. So let us dive in. Now, we can definitely solve this using our sure-shot method of writing out the position vector  r (with the relevant point: P, Q or R as the origin in each case)   and the velocity vector v  of the projectile as functions of time, and then performing the operation r x (m v ) for the angular momentum L . Once we have L , we can analyse the function and comment on the things demanded in the problem. But that method is not what we are here today for. Obviously. If we cannot attack the problem in this basic way, what else do we have? Can we take the cross-product in some other, fancy way? Maybe, but I don't know how. Can we find the perpendicular distance of the particle's instantaneous velocity vector from the given origin (P, Q or R)? That seems quite difficult and lengthy, and rightly so. One beautiful trick to simplify this problem is t...
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From JEE Advanced 2022: Rotating Solenoid

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One of the finest questions of the 2022 JEE Advanced was unfortunately dropped in the evaluation due to a small error. But since the error is a very superficial one, the question remains open for us to enjoy and learn from in its original form. It was Q.15 in Paper-1, the first of the list match questions. Read it and see if you can spot the error. The question is special because it forces us to write all the relevant quantities in vector form. This makes it one of a handful of questions that the JEE paper setters include every year that gradually but surely extend the scope of the exam, by bringing into focus skills that were almost never needed to solve the papers in previous years. Of course, we can do this problem avoiding vector notation completely (and instead proceeding carefully using only the right hand rule for directions), but it would be painful. I know, I tried it and solved it wrong. Twice. So we will do it in the proper way, writing everything vectorially. Make sure you ...
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