Concept:To calculate angular velocity, all spatial dimensions must be equalized. We must convert millimeters and centimeters to a common unit.
Formula:$$ \omega = \frac{v}{r} $$
Solution:- Let's convert both into centimeters.
- Radius \( r = 100 \text{ mm} = 10 \text{ cm} \).
- Speed \( v = 10 \text{ cm/s} \).
- Substitute into formula: \( \omega = \frac{10 \text{ cm/s}}{10 \text{ cm}} \).
- \( \omega = 1 \text{ rad/s} \).
- Since \( 1 \text{ rad/s} \) is not present in Options A, B, or C, the correct choice must be "None of these".
Why other options are incorrect:- Option A happens if you wrongly divide 100 by 10.
- Option B happens if you wrongly divide 10 by 100 (forgetting to convert mm to cm).
- Option C mistakes radians for full revolutions, which are off by a factor of \( 2\pi \).
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