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physics

mechanics

Easy

Question

$text A particle of mass m moves in the end text xy text -plane with a velocity of end text v with not stretchy rightwards arrow on top equals v subscript x i with not stretchy hat on top plus v subscript y j with not stretchy hat on top. text When its position end text text vector is end text r with not stretchy rightwards arrow on top equals x i with not stretchy hat on top plus y j with not stretchy hat on top comma text the angular momentum of the particle about the origin is end text$

$m (x v_{y} + y v_{x}) \hat{k}$
$- m (x v_{y} + y v_{x}) \hat{k}$
$m (y v_{x} - x v_{y}) \hat{k}$
$m (x v_{y} - y v_{x}) \hat{k}$

The correct answer is: $m (x v_{y} - y v_{x}) \hat{k}$

$text We use end text L with not stretchy rightwards arrow on top minus equals r with not stretchy rightwards arrow on top cross times p with not stretchy rightwards arrow on top text - end text L with not stretchy rightwards arrow on top minus equals open vertical bar table attributes columnalign center center center columnspacing 1em rowspacing 4 pt end attributes row cell i with not stretchy hat on top end cell cell j with not stretchy hat on top end cell cell k with not stretchy hat on top end cell row x y 0 row cell m v subscript x end cell cell m v subscript y end cell 0 end table close vertical bar equals i with not stretchy hat on top left parenthesis 0 minus 0 right parenthesis minus j with not stretchy hat on top left parenthesis 0 minus 0 right parenthesis plus k with not stretchy hat on top open parentheses m x v subscript y minus m y v subscript x close parentheses L with not stretchy rightwards arrow on top equals m open parentheses x v subscript y minus y v subscript x close parentheses k with not stretchy hat on top$

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$text For a particle of a mass end text 100 gm text , position and velocity at any instant are given as end text 10 i with not stretchy hat on top plus 6 j with not stretchy hat on top cm text and end text straight v with not stretchy rightwards arrow on top equals 5 straight i with not stretchy hat on top cm divided by straight s text . Calculate the angular momentum about the point end text left parenthesis 1 comma 1 right parenthesis cm.$

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