Kinematics of Circular Motion: Practice Problem & Solution
Assertion (A): Average angular velocity is a scalar quantity. Reason (R): Large angular displacements \( (\Delta \theta) \) is a scalar.
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Kinematics of Circular Motion. Understanding the underlying formula is key to arriving at the correct answer below:
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).
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