The Question is from neet-physics , and it was created by the author NAGA SAI

Question

What is the dimensional formula of angular velocity?

NAGA SAI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: Option A
## CONCEPT FRAMEWORK
**Primary Concept**: Dimensional Analysis
**Related Topics**: Angular Motion, Units and Measurements
**Prerequisites**: Definition of Angular Velocity, Understanding of Dimensional Formulas
## SOLUTION PATHWAY
**Given Information**:
    Angular velocity (ω) is the rate of change of angular displacement (θ).
**Method & Steps**:
    1.  Define Angular Velocity:
        Reasoning: Angular velocity is defined as the rate of change of angular displacement with respect to time.
        Formula/Rule:  $\omega = \frac{\Delta	heta}{\Delta t}$
    2. Determine Dimensions:
        Working: Angular displacement ($	heta$) is a dimensionless quantity (ratio of arc length to radius, both having dimension of length), time (t) has dimension [T].
        Key Point:  Therefore, the dimension of angular velocity is the dimension of angular displacement divided by the dimension of time.
    3. Final Dimension:
        Result:  $\omega = \frac{[1]}{[T]} = [T^{-1}]$
        Verification: This matches the standard dimensional formula for angular velocity.
## OPTION ANALYSIS
[A] ✓: The correct dimensional formula for angular velocity is $[T^{-1}]$.
[B] :x: $[T^{-2}]$ is the dimension of angular acceleration, not angular velocity.
[C] :x: $[LT^{-1}]$ is the dimension of linear velocity, not angular velocity.
[D] :x: $[LT^{-2}]$ is the dimension of linear acceleration, not angular velocity.
## LEARNING AIDS
**Common Mistakes**:
    1. [Error 1]: Confusing angular velocity with linear velocity. [How to avoid]: Remember angular velocity is related to rotational motion, not linear motion.
    2. [Error 2]: Incorrectly assigning dimensions to angular displacement. [How to avoid]: Angular displacement is dimensionless; it's a ratio of two lengths.
**Quick Tips**:
    1. [Helpful shortcut]: Recall that angular velocity is measured in radians per second, where radians are dimensionless, and seconds have dimension [T].
    2. [Memory aid]: Think of angular velocity as 'rotations per unit time'. 'Rotations' are dimensionless, and 'time' has dimension [T].

NAGA SAI · Answer

The correct Option is "$[T^{-1}]$"

NAGA SAI · Answer

$[T^{-2}]$

NAGA SAI · Answer

$[LT^{-1}]$

NAGA SAI · Answer

$[LT^{-2}]$

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