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mechanics

Easy

Question

A uniform circular disc of mass M and radius R rolls without slipping on a horizontal surface. If the velocity of its centre is v₀, then the total angular momentum of the disc about a fixed point P at a height 3R/2 about the centre C.

is always equal to
Increase continuously as the disc moves away
I always equal to
Decrease continuously as the disc moves away

The correct answer is: I always equal to

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em rowspacing 3 pt end attributes row L cell equals I subscript c m end subscript omega with not stretchy rightwards arrow on top plus m v with not stretchy rightwards arrow on top subscript c m end subscript r with not stretchy rightwards arrow on top end cell row blank cell equals fraction numerator M R squared over denominator 2 end fraction times omega left parenthesis negative k with not stretchy hat on top right parenthesis plus M times 3 over 2 R left parenthesis negative j with not stretchy hat on top right parenthesis cross times v subscript 0 i with not stretchy hat on top end cell row L cell equals M R v subscript 0 left parenthesis k with not stretchy hat on top right parenthesis end cell end table$

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