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Q.12 A diwali cracker known as sudarashan chakra works on the principle of thrust. Consider such a toy the centre of which is hinged.The initial mass of the toy is M() and radius is R. The toy is in the shape of a spiral the turns of which are very close (it can be assumed as a disc ).The gases are ejected tangentially from the end of the toy with a constant velocity u relative to the toy. Find the angular velocity ofthe toy when mass remains half.

Q.12 A diwali cracker known as sudarashan chakra works on the principle of thrust. Consider such a toy the centre of which is hinged.The initial mass of the toy is M() and radius is R. The toy is in the shape of a spiral the turns of which are very close (it can be assumed as a disc ).The gases are ejected tangentially from the end of the toy with a constant velocity u relative to the toy. Find the angular velocity ofthe toy when mass remains half.

Grade:12

1 Answers

Ritvik Gautam
85 Points
11 years ago

well.. in this we just need to conserve the angular momentum...

Initially,

Angular momentum = IW

==> MR2U/2R ....................... (v=rw)

==> MRU/2

Finally, assuming the radius to be halfed as mass is halfed..

 

==> MR2 W/8

 

Initial and final angular momentum is conserved

 

==> MRU/2=MR2 W/8

 

==>W=8U/R2

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