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A solid body starts rotating about a sta...

A solid body starts rotating about a stationary axis with an angular acceleration `alpha=(2.0xx10^(-2))trad//s^(2)` here `t` is in seconds. How soon after the beginning of rotation will the total acceleration vector of an arbitrary point of the body form an angle `theta=60^(@)` with its velocity vector?

Text Solution

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`beta=at, (domega)/(dt)=at rArr domega=at dt`
`intdw=intatdt,omega=(at^(2))/2`
`a_(N)=Romega^(2)=Rxx(a^(2)t^(2))/4,a_(T)=R beta=Rat`
`tan 60=a_(N)/a_(T),a_(N)=sqrt3a_(T)`
`Rxx(a^(2)t^(4))/4=sqrt3xxRat, (at^(3))/4=sqrt3`
`:.t^(3)=(4xxsqrt3)/a rArrt=7sec`
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