You always carry 3 wristwatches. One of them is synchronized with your labs atomic clock. Another is running low on battery and is 3 minutes behind, while the third watch is running 6 minutes fast. All were set to the same time when purchased. List the comparative angular velocities of the three watches in order of greatest to smallest.
To determine the comparative angular velocities of the three wristwatches, we need to understand a few key concepts.
Angular velocity refers to how fast an object rotates about an axis. In the case of wristwatches, we can consider the seconds hand as the rotating component that gives us the angular velocity. The angular velocity is measured in radians per unit of time, usually seconds.
Let's break down the information given:
1. The atomic clock watch is synchronized and can be assumed to have the correct time. Thus, its angular velocity can be considered as the average standard angular velocity for a wristwatch.
2. The second watch is running 3 minutes behind the atomic clock time. This means it lags behind the atomic clock watch by 3 minutes or 180 seconds. Consequently, its seconds hand will take longer to complete one full rotation compared to the atomic clock watch. Therefore, its angular velocity will be lesser than the atomic clock watch.
3. The third watch is running 6 minutes fast, meaning it is ahead of the atomic clock time by 6 minutes or 360 seconds. As a result, its seconds hand will rotate faster to complete one full rotation sooner than the atomic clock watch. Thus, its angular velocity will be greater than that of the atomic clock watch.
Based on this information, the order of comparative angular velocities from greatest to smallest would be:
1. Third watch (running 6 minutes fast)
2. Atomic clock watch (synchronized)
3. Second watch (running 3 minutes behind)
To summarize, the third watch will have the highest angular velocity due to running fast, followed by the atomic clock watch with an average angular velocity, and finally, the second watch with the lowest angular velocity as it is running behind.