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Ask iit jee aieee pet cbse icse state board experts Expert Question: rotational mechanix
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doubts.com1 (0)

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the assembly of two discs as shown  in figure is placed on a rough horizontal surface and the front disc is given an initial angular velocity ' w '. determine the final linear and angular velcity when both the discs start rolling, it is given that friction is sufficeient to sustain rolling in the rear wheel from the starting of motion.


    
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i am  waiting for the reply..........................any one please...........................................                  

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shreyasnivas (256)

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hey i cant understand the diagram.. why will the second sphere move?

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the front disc is given an initial angular velocity w.


 


this question is from arihant..............................................

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varun.tinkle (1054)

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CANT UNDERSTAND THE QUES
IN THE END WHEN THEY WILL HAVE THE SAME VELOCITY THEN U WANT TO FIND OUT OR OTHERWISE

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after both the discs start rolling ,          what  is their final linear and angular  velocity.


 


ans:       angular velocity:   w / 6 ,      


               linear velocity   :  w R / 6 .


 


any experts ...........please give the solution  ..... .... ............  i am waiting  !!!!!!!!

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varun.tinkle (1054)

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SEE
I AM ASSUMING THAT THEY R CONNECTED BY STRINGS THEN
LETS CONSIDER THE FIRST WHEEL
SINCE IT IS MOVING BACKWARDS IT HAS A TENDENCY TO SLLIP SO FRICTION WILL ACT IN THE FORWARD DIRECTION
f+T=MA
FR=IA/R
FOR THE 2 ND BLOCK
TENSION WILL ACT IN THE FORWARD DIRECTION AND TO PREVENT RELATIVE MOTION
FRICTION WILL ACT IN THE BACKWARDS DIRECTION AND IT WILL ALSO PRODUCE A TORQUE
T-F=MA
FR=IA

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varun.tinkle (1054)

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pls verify my methods

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hey varun,


i solved this using ur equations but i am not getting the answer.


once u try urself,,,,


i didnot understand the first equation    f+T=MA,


 


becos for the right disc which is rotating with an  angular velocity w ,  the friction acts in the forward direction(i.e, rightward)  and the tension is acting along the string (leftward)......and  hence the equation comes to be


         f - T= MA

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varun.tinkle (1054)

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YES IT IS F-T
IN TH FIRST EQUATION



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even if it is f-T=MA  u wiill not get the answer. first  u try it and then give the reply completely.......


 


any experts please answer to my question. i am  not getting it.................


 


i am waiting only for the complete solution.................and not anything else......................


 


 

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varun.tinkle (1054)

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I SOLVED IT
SEE SINCE THERE IS NO EXT FORCE ACTING ON THE SYSTEM SINCE THE FRICTIONAL FORCES CANCEL EACH OTHER AS IT IS SHOWN Y THE EARLIER POSTS. TENSION IS AN INTERNAL FORCE AND NEE DNOT BE CONSIDERED
SO THE PRINCIPLE OF CONSERVATION OF ANGULAR MOMENTUM CAN BE APPLIED
INITIAL ANGULAR MOMENTUM IS IW
FINALLY THE ANGULAR AND THE LINEAR VELOCITIES OF BOTH THE SPHERE WILL BE EQUAL SINCE THEY R CONNECTED BY THE SAME STRING
SO THE ANGULAR MOMENTUM OF ONE OF THEM
IS IW2+MVR
W2=VR SINCE THE SPHERE IS RLLING
IVR+MVR=1/2MR^2*V*R+MVR
=1/2MVR+MVR=3/2MVR
SO THE ANGULAR MOMENTUM OF BOTH THE SPHERES R 3MVR
IW=3MVR
1/2MR^2W=3MVR
V=WR/6
COZ OF ROLLING
V=RW W=V/R=WR/6R=WR/6
PLZ RATE ME
COZ IT TOOK ME 5 HRS TO SOLVE IT
CHEERS

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The crown less again shall be king.

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