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?

Answer

7

Explanation

`beta = at , " (d omega)/(dt) = at implies d omega = at dt `
`int d omega = int at dt , omega = (at^(2))/(2)`
`a_(N) = R omega^(2) = R xx (a^(2) t^(2))/(4)`

`a_(T) = R beta = R at `
`tan 60^(@) = (.^(a)N)/(.^(a)T) , a_(N) = sqrt3 a_(T)`
`R xx (a^(2)t^(4))/(4) = sqrt3 xx R at , (at^(3))/(4) = sqrt3`
`therefore " " t^(3) = (4 xx sqrt3)/(a) implies t = 7` sec