A solid body starts rotating about a stationary axis with an angular acceleration `alpha=kt`, where `k` is a constant. How soon after the beginning of motion will the total acceleration vector of an arbitrary point of the body form an angle `60^(@)` with its velocity vector?

Explanation

`alpha=kt`
`(domega)/(dt)=kt`
`int_(0)^(omega)domega=k int_(0)^(t)t dt`
`omega=(kt^(2))/(2)`
`a_(c)=omega^(2)r=(k^(2)t^(4)r)/(4)`
`a_(t)=ralpha=ktr`
`tantheta=(a_(c))/(a_(t))`
`tan60^(@)=(k^(2)t^(4)r)/(4)xx(1)/(ktr)`
`sqrt3=(k)/(4)t^(3)`
`t^(3)=(4sqrt3)/(k)`
`t=((4sqrt3)/(k))^((1)/(3))`