Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Two coins

  1. Aug 31, 2003 #1
    Imagine rolling a coin with a radius of 1 unit on a flat surface. To get translated 2[pi] units, the coin must obviously roll 1 revolution. (the angle swept is 2[pi] and the arc length covered equals to 2[pi]*r = 2[pi]*1 = 2[pi].

    Now imagine rolling a coin on another stationary coin with the same radius (circumference = 2[pi] = length of the first track). How can it be that it requires 2 revolutions? Is it because the real track isn't the black coin but the trace of the circle's center when moving (which equals 4[pi])?

    It makes me feel uneasy... Can anyone give a satisfactory/intuitive explanation?
     

    Attached Files:

  2. jcsd
  3. Aug 31, 2003 #2
    See the attached image btw...
     
  4. Aug 31, 2003 #3
    It doesn't require two revolutions, only one.

    When any coin rolls along its edge on a flat surface, the distance it travels in 1 revolution is always 2*pi*r units. When you roll an coin along the edge of an identical coin, 1 revolution is still 2*pi*r units because to the coin, the surface is still flat. This means it still only takes the coin 1 revolution to roll around the other coin!

    Just imagine laying out the circumference of a coin on a flat table. This length will be 2*pi*r units long. The other coin simply rolls along this = 1 revolution for the rolling coin.

    If I understood your question correctly.
     
  5. Aug 31, 2003 #4

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    The coin experiences one revolution because it rolled a distance of 2π radians, and the coin experiences one revolution because it was rotated 2π radians around the central coin. Add them up and you get two revolutions!

    If you spun around in just the right way while doing the experiment, you'd see it experience three revolutions. :smile:
     
  6. Aug 31, 2003 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Uh, Hurkyl, this was a joke,right? (just checking)
     
  7. Aug 31, 2003 #6

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Grr, I'm thinking "rotation" while saying "revolution". :frown:

    From the overhead POV, the coin undergoes two rotations through 1 revolution!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Two coins
  1. Coins and Trays (Replies: 0)

  2. Coins problem (Replies: 2)

  3. Flipping coins (Replies: 5)

  4. Coins problem (Replies: 3)

Loading...