Angular Velocity and Displacement Nature – Rankers Physics

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.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

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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