NEET Kinematics of Circular Motion MCQs & PYQs

Instantaneous angular velocity \( \vec{\omega} \) is a vector. However, finite angular displacement \( \Delta \theta \) is not a vector, but a scalar, as stated in Reason (R). Therefore, if average angular velocity is defined as the scalar \( \Delta \theta / \Delta t \), then Assertion (A) is considered true. In this context, both (A) and (R) are true, and (R) provides the explanation for (A).

Angular velocity \(\omega = \frac{2\pi}{\text{T}}\). For a seconds hand, \(\text{T} = 60\text{ s}\). Thus, \(\omega = \frac{2\pi}{60} = \frac{\pi}{30}\text{ rad/s}\). Both assertion and reason are true, and the reason correctly explains the assertion.

Concept: Definition of angular acceleration. Formula: $\alpha = \frac{\omega_2 - \omega_1}{t}$. Solution: Converting rpm to rad/s and substituting values gives $\alpha = 4\pi\text{ rad/s}^2$.

Concept: Kinematic equation for angular motion. Formula: $\alpha = \frac{\Delta \omega}{t}$. Solution: $\omega_1 = 12\pi$, $\omega_2 = 40\pi$, yielding $\alpha = \frac{28\pi}{14} = 2\pi\text{ rad/s}^2$.

Concept: Rotational kinematics equation. Formula: $\theta = \omega_0 t + \frac{1}{2}\alpha t^2$. Solution: $\theta = (2.0)(2) + \frac{1}{2}(3.0)(2)^2 = 4 + 6 = 10\text{ radians}$.