# How does this clock work ?

1. Jan 24, 2013

### hms.tech

1. The problem statement, all variables and given/known data
see attachment

2. Relevant equations

θ= ω*τ

3. The attempt at a solution

1.Is this a proper clock, will it show the correct time as any normal clock ?
2.what is the angular displacement of one of the clock hand when it moves from 1 to 2.
Is this angular displacement constant every 5 minutes (ie from 1 to 2 , 2 to 3 , 3 to 4 etc ).

2. Jan 24, 2013

### Curious3141

1. For the purposes of this question, you may assume that the *hour* will be shown exactly on the hour, ditto with the minutes in multiples of five. The interpolations between markings may not be exact, but you needn't concern yourself with this.

2. What would this be in a "regular" circular clock? Would you expect it to be different here?

3. Why wouldn't it be?

3. Jan 24, 2013

### hms.tech

we'll consider the time in seconds for easiness.

More help required ...

4. Jan 24, 2013

### Staff: Mentor

When a hand points to 12, it forms an angle with the vertical of 0°.
When a hand points to 1, it forms an angle with the vertical of ??°
When a hand points to 2, it forms an angle with the vertical of ??°

5. Jan 24, 2013

### hms.tech

When it points to one, it forms an angle of ∏/6
When it points to two, it forms and angle with the vertical of ∏/3

6. Jan 24, 2013

### Staff: Mentor

So you can now on the clock face draw some triangles showing lengths and angles, for a hand pointing to 1, and also for it pointing to 2.

7. Jan 24, 2013

### hms.tech

Aren't these angles only applicable to a normal "round clock" ?

8. Jan 24, 2013

### Staff: Mentor

Each hand moves at a constant angular rotation, like an ordinary clock, we are told.

9. Jan 24, 2013

### LCKurtz

Draw a round clock in the same picture centered between 6 and 12 and extend the radii.

10. Jan 24, 2013

### Curious3141

These angles are applicable to this clock, because you're told the hands move like a normal (round) clock.

You might find it easier to visualise the problem if you express everything in degrees. Consider the hand at position "n" and then at position "n+2" (two markings apart). What's the angle between those two positions?

Do you see a special triangle here? This makes things quite easy, along with some very simple trig.

You could take up LCKurtz's suggestion to draw a round clock, but personally, I think it might complicate things if you clutter the figure with a circle. I would suggest just drawing the rectangle and the various triangles within it and treating the problem as simple geometry and trig.