A solid body rotates about a stationary axis so that its angular velocity depends on the rotational angle ϕ as ω = ω 0 - k ϕ where ω 0 and k are positive constants. At the moment t = 0 , ϕ = 0 , find the time dependence of rotation angle

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Correct answer: C. ω 0 k 1 - e - k t

&#8757; &#969; = &#969; 0 - k &#981; or d &#981; d t = &#969; 0 - k &#981; Or &#8747; 0 &#981; d &#981; &#969; 0 - k &#981; = &#160; &#8747; 0 t d t Or - 1 k &#160; ln &#969; 0 - k &#981; 0 &#981; = t Or ln &#969; 0 - k &#981; &#969; 0 = &#160; - k t &#8756; &#981; = &#969; 0 k &#160; 1 - e - k t

A solid body rotates about a stationary axis so that its angular velocity depends on the rotational angle ϕ as ω = ω 0 - k ϕ where ω 0 and k are positive constants. At the moment t = 0 , ϕ = 0 , find the time dependence of rotation angle

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