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Understanding angular velocity in terms of "revolutions per hour" is a matter of recognizing how complete cycles occur in a specific period. When dealing with the second hand of the clock, we know it makes one full revolution every minute. However, to express this in revolutions per hour, we must understand the basic math behind it.

- Each revolution takes 60 seconds. Therefore, in one minute, it will complete exactly one revolution.
- In one hour, which is 60 minutes, the second hand therefore makes 60 full revolutions.

Hence, the angular velocity of the second hand, when expressed in terms of revolutions per hour, is 60 rev/hr. This means the second hand circles the clock face 60 times in a single hour.

"Degrees per minute" is another practical way to measure angular velocity, indicating how many degrees an object covers per minute. For rotating objects like the second hand of a clock, this measurement helps visualize its speed in terms of angles covered rather than full circles.

- One full revolution equals 360 degrees. Therefore, if the second hand completes one revolution every minute, it covers 360 degrees in that time.

Breaking this down further:
- Since the second hand completes 60 revolutions per hour, in one minute, it completes one revolution spreading over 360 degrees.

Thus, the angular velocity of the clock's second hand in degrees per minute is 360 deg/min, illustrating a per-minute sweep of the clock face by 360 degrees, equivalent to one complete circle around the clock.

"Radians per second" is a unit that is part of the radian system, commonly used in mathematical and scientific computations. It provides another perspective of evaluating angular velocity, by expressing it in radians, a standard mathematical unit.

- To understand this conversion, remember that one full revolution is equal to \(2\pi\) radians.
- Given the second hand makes one revolution in 60 seconds, to calculate radians per second, start with previously established revolutions per hour.

Here's how to arrive at radians per second for the second hand:
- Starting from 60 rev/hr, multiply by \(\frac{2\pi}{1}\) rad per rev. Then convert hours to seconds by recognizing that one hour equals 3600 seconds:
- This gives the formula \[\text{rad/s} = 60 \times \frac{2\pi}{1} \times \frac{1}{3600} = \frac{\pi}{30} \text{ rad/s}.\]

Therefore, the second hand rotates at \(\frac{\pi}{30}\) radians per second, offering a precise measure of its rotational speed in radians over time.