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Homework Statement
A solid body rotates with deceleration about a stationary axis with an angular deceleration
[tex]\beta[/tex] [tex]\propto[/tex] [tex]\sqrt{\varpi}[/tex] , where [tex]\varpi[/tex] is the angular velocity. Find the mean angular velocity of the body averaged over the whole time of the rotation if at the initial moment of time the angular velocity was [tex]\varpi[/tex]0
Homework Equations
[tex]\varpi[/tex]f = [tex]\varpi[/tex]i + [tex]\beta[/tex]t
[tex]\varpi[/tex]avg = [tex]\varphi[/tex]/t
The Attempt at a Solution
The given answer is <[tex]\varpi[/tex]> = [tex]\varpi[/tex]0/3