Concept:To find the final angular velocity using angular acceleration and displacement, we use the third equation of rotational motion.
Formula:$$ \omega_f^2 = \omega_i^2 + 2\alpha\theta $$
Solution:- The wheel starts from rest, so \( \omega_i = 0 \).
- Convert revolutions to radians: \( \theta = 10 \text{ rev} \times 2\pi = 20\pi \text{ rad} \approx 62.83 \text{ rad} \).
- Plug in the values: \( \omega_f^2 = 0 + 2(4.0)(20\pi) = 160\pi \).
- \( 160 \times 3.1416 \approx 502.6 \).
- Take the square root: \( \omega_f = \sqrt{502.6} \approx 22.4 \text{ rad/s} \).
- The closest option is 22 rad/s.
Why other options are incorrect:- Option A, Option C, Option D occur if one forgets to multiply by \( 2\pi \) for radians or forgets to take the final square root.
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