A particle is performing uniform circular motion. If ' $\theta^{\prime},{ }^{\prime} \omega^{\prime},{…

A particle is performing uniform circular motion. If ' $\theta^{\prime},{ }^{\prime} \omega^{\prime},{ }^{\prime} \propto^{\prime}$ and 'a' are its angular displacement, angular velocity, angular acceleration and centripetal acceleration respectively, then which of the following is 'WRONG'? (' $\mathrm{v}$ ' is its linear velocity )
  1. $\overrightarrow{\mathrm{v}} \perp \overrightarrow{\mathrm{a}}$
  2. $\vec{\omega} \perp \overrightarrow{\mathrm{V}}$
  3. $\vec{\omega} \perp \vec{\alpha}$
  4. $\vec{\omega} \perp \overrightarrow{\mathrm{a}}$

Solution

For a particle performing uniform circular motion, the following relationships hold true: 1. Angular displacement $\theta$ is related to the angle through which the particle moves. 2. Angular velocity $\omega$ is the rate of change of angular displacement. 3. Angular acceleration $\alpha$ is the rate of change of angular velocity. 4. Centripetal acceleration $a_c=\frac{v^2}{R}$, where $v$ is the linear velocity and $R$ is the radius of the circular path. The incorrect statement is: - Option (3): This is identified as the wrong statement in the solution.

Asked in: MHT CET 2020 (12 Oct Shift 2)

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