If angular acceleration= -mB theta/I

How is Omega that is angular velocity= √(mB/I)

Asked by prakriti12oct | 19th Feb, 2020, 12:22: AM

Expert Answer:

If acceleration is constnant C  times acceleration and C is negative ,
then the motion is SHM and magnitude of C is square of angular frequency.
 
x = A sin(ωt )  ,  ( dx/dt ) = Aω cos(ωt)  , 
 
( d2x/dt2 ) = - Aω2 sin(ωt) = -ω2 [ A sin(ωt) ] = -ω2 x
 
Hence in the expression begin mathsize 14px style fraction numerator d squared theta over denominator d space t squared end fraction space equals space minus space open parentheses fraction numerator m space B over denominator I end fraction close parentheses space theta end style  , 
we get begin mathsize 14px style omega squared equals space fraction numerator m B over denominator I end fraction space space o r space space omega space equals space square root of fraction numerator m space B over denominator I end fraction end root end style

Answered by Thiyagarajan K | 19th Feb, 2020, 11:38: AM

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