A thin uniform rod of length 2 m, cross-sectional area A and density d is rotated about an axis passing through the centre and perpendicular to its length with angular velocity ω. If the value of ω in terms of its rotational kinetic energy E is √(α E)/(Ad), then the value of α is .

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3. The rod's mass is its volume times its density: M=A L d=A(2)d=2Ad. About a perpendicular axis through the centre: I=(ML²)/(12)=((2Ad)(4))/(12)=(2Ad)/3. Rotational kinetic energy: E=1/2Iω²=1/2·(2Ad)/3ω²=(Ad ω²)/3. Rearranging: ω²=(3E)/(Ad). ω=√(3E)/(Ad), so α=3.

A thin uniform rod of length 2 m, cross-sectional area A and density d is rotated about an axis passing through the centre and perpendicular to its length with angular velocity ω. If the value of ω in terms of its rotational kinetic energy E is √(α E)/(Ad), then the value of α is ______.

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