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Finding length of minute hand of clock

  1. Jun 24, 2013 #1

    QuantumCurt

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

    The minute hand of a clock travels 6.28 inches in 15 minutes. Find the length of the minute hand. Approximate to the nearest inch, if necessary.




    3. The attempt at a solution

    I figured the arc length to be [itex]\frac{\pi}{2}[/itex] because it's traveled one quarter of the way around the clock.

    I set the equation up like this-

    [tex]\frac{\pi/2}{15}x=6.28[/tex]

    Then I solve for x by multiplying by the reciprocal, and I'm getting 59.97.

    This was a question on a test I had earlier today, and when I did it then, I got approximately 15.001 or something like that. That answer didn't seem right to me, and the answer I'm getting now doesn't seem anymore right. I can't remember exactly how I set it up. What am I doing wrong? The rest of the test was simple, this was the only one that threw me off.
     
  2. jcsd
  3. Jun 24, 2013 #2

    Mark44

    Staff: Mentor

    Why are you dividing by 15?
     
  4. Jun 25, 2013 #3

    QuantumCurt

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    I had been trying to use a linear speed formula to find the radius, but as I've thought about it more it made less and less sense.

    Should I have found the circumference by multiplying the 6.28 by 4 to get the entire circumference of the circle, then divide by 2pi?
     
  5. Jun 25, 2013 #4

    verty

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    The pertinent fact is that circumference = 2π * radius; from this you can find the length of one quarter of the circumference. In general you want to find a formula including the unknown and the known. This is the algebraic way of thinking - get a formula that for conceptual reasons you know is correct, then plug in the numbers with less chance of making a mistake.
     
  6. Jun 25, 2013 #5

    lalo_u

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    I agreed Verty.

    You may start with the definitlion of [itex]\pi=\frac{\mathcal{C}}{2R}[/itex], where [itex]\mathcal{C}[/itex] is the circumference lenght.

    Then, since you have the lenght of a quarter of the circumference, can clear the radio.
     
  7. Jun 25, 2013 #6

    HallsofIvy

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    All that is relevant is that [itex](\pi/2)r[/itex] is the length of a quarter circle arc. The time it takes to travel that is irrelevant. You only need the fifteen minutes to know that the minute hand traveled a quarter circle.
     
  8. Jun 25, 2013 #7

    QuantumCurt

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    So then I would want to set it up like-6.28(4)/2pi? So...approximately 8 inches?
     
  9. Jun 25, 2013 #8

    lalo_u

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    You're dividing a quarter of an arc between a full arc angle...
     
  10. Jun 25, 2013 #9

    Mark44

    Staff: Mentor

    6.28 ≈ 2##\pi##, so the expression above simplifies to approximately 4.
     
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