Calculating angular displacement of clockhands

In summary, the angular displacement of a hand that goes around a clock once is 2π radians, twice is 4π radians, and half way around is π radians.
  • #1
DeeAussie
4
0

Homework Statement


What is the a.d of each of the following hands of a clock in 1h?
the second and?
the minute hand?
the hour hand?


Homework Equations


That's what I'm looking for


The Attempt at a Solution


I'm having trouble getting it on paper, just a description of how one of you might crack this would be wonderful.


thank you
 
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  • #2
Going around a circle exactly once corresponds to [tex] 2 \pi [/tex] radians (of angular displacement). Going around the circle twice is twice that. Going half way around the circle is 1/2 that, and so on.

So what's the angular displacement (i.e. how many radians are traversed) of a hand that goes around exactly once? One that goes around 60 times? And 60 x 60 times?
 

Related to Calculating angular displacement of clockhands

1. How do you calculate the angular displacement of clock hands?

The angular displacement of clock hands can be calculated by first determining the angle between each hour on the clock face. Each hour represents 30 degrees on the clock face. Next, determine the position of the clock hands and subtract the smaller angle from the larger angle. This will give you the angular displacement of the clock hands.

2. What is the formula for calculating angular displacement?

The formula for calculating angular displacement is θ = s/r, where θ is the angular displacement, s is the arc length, and r is the radius of the circle.

3. Can the angular displacement of clock hands be negative?

Yes, the angular displacement of clock hands can be negative. This occurs when the clock hands move in a counterclockwise direction.

4. How is the angular displacement of clock hands different from the angular velocity?

The angular displacement of clock hands measures the change in the angle of the clock hands over a period of time, while the angular velocity measures the rate of change of the angular displacement. In other words, the angular velocity takes into account the time it takes for the clock hands to move from one position to another.

5. How can the angular displacement of clock hands be used in real-life applications?

The angular displacement of clock hands can be used in various fields such as astronomy, navigation, and engineering. In astronomy, it can be used to track the movement of celestial bodies. In navigation, it can be used to determine the direction and distance traveled. In engineering, it can be used in the design and analysis of rotating machinery.

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