Physics
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.

  1. Increase continuously as the disc moves away
  2. Decrease continuously as the disc moves away
  3. is always equal to   
  4. I always equal to  

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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