Question
A solid body rotates about a stationary axis so that its angular velocity depends on the rotational angle `phi` as `omega = omega_0 - k phi` where `omega_0` and k are positive constants . At the moment t = 0, `phi ` = 0. Find the time dependence of rotation angle :
Answer: Option C
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`because` ` omega = omega_0 - k phi`
or ` (d phi)/(dt) = omega_0 - k phi`
or `int_0^phi (d phi)/(omega_0 - k phi)` = `int_0^1 dt`
or `- 1/k [In (omega_0 - k phi)]_0^phi` = t
or `In ((omega_0 - k phi)/(omega_0) = - kt`
`:.` ` phi = omega_0/k (1 - e^-(kt))`
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