A ceiling fan starts rotating from rest with angular acceleration varying as #A=D^(1/2)# where D is the angular displacement magnitude.how does its angular velocity vary with respect to D?

1 Answer
P dilip_k
Jan 5, 2018

Angular acceleration is represented by #A# ,angular displacement by #D# and angular velocity by #omega#. If #t# represents time then
#omega=(dD)/(dt)#

#A=(domega)/(dt)=(domega)/(dD)xx(dD)/(dt)#

#=>A=(domega)/(dD)xxomega#

#=>D^(1/2)=(domega)/(dD)xxomega#

#=>omegadomega=D^(1/2)dD#

Integrating
#=>int_0^omegaomegadomega=int_0^DD^(1/2)dD#

#=>omega^2/2=2/3D^(3/2)#

#=>omega^2=4/3D^(3/2)#

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