Park Burton
08/24/2024 · Elementary School
Find the angular speed \( \omega \) of the minute hand of a clock. The angular speed is \( \square \) radian per min.
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To find the angular speed \( \omega \) of the minute hand of a clock, we need to determine how much angle the minute hand sweeps in a given time period.
The minute hand completes one full revolution (which is \( 2\pi \) radians) in 60 minutes. Therefore, the angular speed \( \omega \) can be calculated using the formula:
\[
\omega = \frac{\text{Total angle in radians}}{\text{Time in minutes}}
\]
Substituting the values:
\[
\omega = \frac{2\pi \text{ radians}}{60 \text{ minutes}} = \frac{\pi}{30} \text{ radians per minute}
\]
Thus, the angular speed \( \omega \) of the minute hand of a clock is
\[
\frac{\pi}{30} \text{ radians per minute}.
\]
Quick Answer
The angular speed \( \omega \) of the minute hand of a clock is \( \frac{\pi}{30} \) radians per minute.
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