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Circular Velocity

  1. Sep 13, 2003 #1
    The speed of the tip of the minute hand on a town clock is 0.00112 m/s.
    What is the speed of the tip of the second hand of the same length? Answer in units of m/s.

    I don't even know where to start. We've been doing centripetal acceleration but I don't know how this even fits in to that?
    I was thinking I could somehow set them equal to each other because of the same length that they have - but not sure how to go about that.

    If anyone could please help?
     
  2. jcsd
  3. Sep 13, 2003 #2
    I'm assuming what you know what angular velocity is. It is related to speed by

    v = ω*r

    where r is the radius. The angular velocity is just ΔAngle/ΔTime.

    So in this case the radius or length of the minute hand can be calculated as

    r = v/ω

    this is also the length of the second hand, seeing as their lengths are the same. The minute hand does one revolution every hour, so

    ΔAngle = 2*PI
    ΔTime = 1 hr = 60*60 s = 3600s

    so for the minute hand ω = PI/(1800s) = PI / 1800 s^-1

    Let V and Ω be the speed and angular velocity respectively of the second hand

    so, r = V/Ω

    seeing as their lenghs are equal we have

    V/Ω = v/ω
    V = v * Ω / ω

    seeing as the second hand goes around the clock once every 60 seconds then its angular velocity is PI/30 s^-1.

    So, V = 0.00112 m/s * ( PI/30 s^-1 ) / ( PI / 1800 s^-1 )
    V = 0.0672 m/s

    so the speed of the second hand is 0.0672 m/s.
     
    Last edited by a moderator: Sep 13, 2003
  4. Sep 13, 2003 #3
    Haha. I'm still sort of confused about what you did since I'm taking calculus I just now and it's kind of hard to do Calculus based Physics. I'm trying to use the velocity that you gave me for the second hand to find the centripetal acceration of the tip of the second hand? I'm also confused as to how you got Angle/Time from the radius equation.
     
  5. Sep 13, 2003 #4
    The problem can also be solved by noting the fact that after one revolution of the minute hand around the clock the second hand has made sixty revolutions. Seeing as the second and minute hands are of equal length, then it follows that the speed of the second hand is sixty times faster than the speed of the minute hand! Do the calculations and you'll find this matches the answer above.
     
    Last edited by a moderator: Sep 13, 2003
  6. Sep 14, 2003 #5
    I'm a little confused. What does the second hand measure: hours or seconds? If it's seconds the answer is what MathNerd just said, but if it's hours then the speed is 24 times smaller.
     
  7. Sep 14, 2003 #6

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Believe it or not, Sonty, the second hand measures seconds!!

    That's why it's CALLED a second hand!!

    Sorry if this sounds sarcastic, but I've had a hard weekend, someone has to pay, and you stuck your head up!!

    (What mathnerd is REALLY saying is that, since the second hand makes a complete circle of the clock face every 60 seconds (one minute) while the minute hand does so every 60 minutes (one hour), the second hand is going 60 times as fast: it's speed is

    60(0.00112 m/s)= 0.0672 m/s.)
     
  8. Sep 14, 2003 #7
    Gosh I'm a moron. "second" doesn't always mean 2nd. It seems my weekend was even worse if I couldn't make that connection and writing them next to each other didn't help. Need time away from this damn computer, need real life, need using this english thing more, need....[zz)]
     
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