A particle is moving along a circular path. The angular velocity, linear velocity, angular accel...

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A particle is moving along a circular path. The angular velocity, linear velocity, angular acceleration, and centripetal acceleration of the particle at any instant, respectively, are \( \vec{\omega}, \vec{v}, \vec{\alpha} \), and \( \vec{a}_{c} \). Which of the following relations is not correct?
(1) \( \vec{\omega} \perp \vec{v} \)
(2) \( \vec{\omega} \perp \vec{\alpha} \)
(3) \( \vec{\omega} \perp \vec{\alpha}_{c} \)
(4) \( \vec{v} \perp \vec{\alpha}_{c} \)
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