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Physics - Rotation Question with Solution | TestHub

PhysicsRotationRotational KinematicsEasy2 minQB

PhysicsEasysingle choice

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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Solution:

$∵$ $ω = ω_{0} - k ϕ$ or $\frac{d ϕ}{d t} = ω_{0} - k ϕ$

Or $\int_{0}^{ϕ} \frac{d ϕ}{ω_{0} - k ϕ} = \int_{0}^{t} d t$

Or $- \frac{1}{k} {[\ln (ω_{0} - k ϕ)]}_{0}^{ϕ} = t$

Or $\ln (\frac{ω_{0} - k ϕ}{ω_{0}}) = - k t$

$∴$ $ϕ = \frac{ω_{0}}{k} (1 - e^{- k t})$

Stream:JEESubject:PhysicsTopic:RotationSubtopic:Rotational Kinematics

⏱ 2mℹ️ Source: QB

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