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Relation between Linear and Angular Speed

A particle is...

Question

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 $\to ω, \to v, \to α$ and $_{c}$ . Which of the following relations is not correct?

\to ω ⊥ \to v

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\to ω ⊥ \to α

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\to ω ⊥_{c}

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\to v ⊥_{c}

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Solution

The correct option is B $\to ω ⊥ \to α$
We know that,
$\to v = \to ω \times \to r$
where $\to v$ is tangential velocity and $\to ω$ is the rotational speed.
$\Rightarrow \to v ⊥ \to ω$ ,

$\to v$ is along tangent of the circle,
$_{c}$ is towards centre of circle.
$\to ω$ is perpendicular to plane of circle.
So, $\to v ⊥_{c}$ and $\to ω ⊥ a_{c}$

$\to ω$ as angular velocity and $\to α$ is angular acceleration
$\Rightarrow \to ω, \to α$ are either parallel or anti parallel to each other, so $\to ω$ is not perpendicular to $\to α$ .

Hence option B is the correct option.

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