Angular Velocity of Minute-Hand of a Watch

Angular velocity is a measure of the rate of change of angular displacement of an object with respect to time. In the case of a watch, the minute-hand undergoes angular displacement as it moves around the dial. The angular velocity of the minute-hand can be calculated using the formula:

Angular velocity = Angular displacement / Time taken

The angular displacement of the minute-hand is equal to 360 degrees, as it completes one full rotation around the dial in 60 minutes. Therefore, the angular displacement can be expressed as:

Angular displacement = 360 degrees

The time taken for the minute-hand to complete one full rotation is 60 minutes. However, we need to convert this time to seconds to calculate the angular velocity. Therefore, the time taken can be expressed as:

Time taken = 60 minutes x 60 seconds/minute = 3600 seconds

Substituting these values in the formula, we get:

Angular velocity = 360 degrees / 3600 seconds = 0.1 degrees/second

This means that the minute-hand of a watch moves at a constant angular velocity of 0.1 degrees per second.

Factors affecting angular velocity

There are several factors that can affect the angular velocity of the minute-hand of a watch. These include:

- The size of the watch dial: A larger dial will require the minute-hand to travel a greater distance to complete one full rotation, which will result in a lower angular velocity.
- The weight of the minute-hand: A heavier minute-hand will require more energy to move, which will result in a lower angular velocity.
- Friction: Friction between the minute-hand and the watch mechanism can cause the minute-hand to move at a slower angular velocity.
- Temperature: Extreme temperatures can affect the performance of the watch mechanism and cause the minute-hand to move at a slower or faster angular velocity.

Conclusion

The angular velocity of the minute-hand of a watch is a measure of the rate of change of angular displacement of the minute-hand with respect to time. It can be calculated using the formula angular velocity = angular displacement / time taken. The angular velocity of the minute-hand of a watch is affected by several factors, including the size of the watch dial, the weight of the minute-hand, friction, and temperature.