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bhanuveer danduboyina Grade: 12th Pass
        The magnitude of displacement of a particle moving in a circle of radius 'a' with constant angular speed 'w' varies with time 't' as:  
6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

R = acos@ (i) + asin@ (j)       ................1        


R is the position vector of particle at any time performing circular motion...


@ is angular displacement


 


w = @/t


@ = wt         ..............2


from 1 & 2


Rt = acoswt (i) + asinwt (j)          .............3


at t = 0 ,


Ro = a (i)             ..............4


 


displacement = Rt - Ro = a(coswt-1) (i) + a(sinwt) (j)


magnitude =[ (a2(coswt-1)2 + a2(sinwt)2]1/2


                =  [2a2 - 2a2coswt]1/2


                = a[2(1-coswt)]1/2


 


now , coswt = (1-2cos2(wt/2)) , after putting this in above eq


  magnitude = 2a[cos2(wt/2)]1/2


                  =2acos(wt/2)


this is the required result ,


 


approve if u like my ans

6 years ago
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