Concept:To convert from revolutions per minute (rpm) to radians per second (rad/s), we must apply conversion factors for both the angular displacement and the time.
Formula:$$ \omega = \text{rpm} \times \frac{2\pi}{60} $$
Solution:- Given \( 400 \text{ rpm} \).
- Multiply by \( 2\pi \) to convert revolutions to radians: \( 400 \times 2\pi = 800\pi \text{ rad/min} \).
- Divide by 60 to convert minutes to seconds: \( \omega = \frac{800\pi}{60} \).
- Cancel the zeroes: \( \frac{80\pi}{6} \).
- Divide top and bottom by 2: \( \omega = \frac{40\pi}{3} \text{ rad/s} \).
Why other options are incorrect:- Option A is half of the correct speed (as if one forgot to multiply by 2 for the radians).
- Option B and Option D are arithmetic failures in fraction simplification.
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