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Physics

Mechanics

Easy

Question

A disc of mass m and radius R moves in the X-Y plane as shown in figure. The angular momentum of the disc about the origin O at the instant shown is

$- \frac{5}{2} m R^{2} ω \hat{k}$
$\frac{7}{3} m R^{2} ω \hat{k}$
$- \frac{9}{2} m R^{2} ω \hat{k}$
$\frac{5}{2} m R^{2} ω \hat{k}$

The correct answer is: $negative 5 over 2 m R squared omega k with not stretchy hat on top$

$table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell L with not stretchy rightwards arrow on top equals I subscript C M end subscript omega with not stretchy rightwards arrow on top plus m left parenthesis r with not stretchy rightwards arrow on top cross times v with not stretchy rightwards arrow on top right parenthesis end cell row cell L with not stretchy rightwards arrow on top equals 1 half M R squared omega k with not stretchy hat on top plus M left parenthesis 4 R i with not stretchy hat on top plus 3 R j with not stretchy hat on top right parenthesis cross times left parenthesis R omega right parenthesis i with not stretchy hat on top end cell row cell equals fraction numerator M R squared over denominator 2 end fraction omega k with not stretchy hat on top minus 3 M R squared omega k with not stretchy hat on top end cell row cell L with not stretchy rightwards arrow on top subscript text tot end text end subscript equals fraction numerator negative 5 over denominator 2 end fraction M R squared omega k with not stretchy hat on top end cell end table$

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