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

Is uniform circular motion perpetual?

  1. Aug 4, 2013 #1
    If i took my pencil to a place in space without gravity or air resistance and i spun it, would it spin forever? I mean its undergoing a centripetal acceleration, so energy has to come from somewhere to keep it spinning right? (and of course this is not meant to be an idea for perpetual motion, i know those are against the rules)
     
  2. jcsd
  3. Aug 4, 2013 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Things move for a long time in outer space not because they are always consuming energy, but because the vacuum of space offers no resistance to movement, unlike on earth. If you spin a pencil in space, the energy imparted in the initial spin is not diminished by any friction acting on the pencil due to its spinning motion. As Newton said, "A body in motion tends to stay in motion, unless acted upon by an external force."
     
  4. Aug 4, 2013 #3

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    If nothing else happens - yep.

    Nope. The input of energy occurred at the start when you spun it up.

    This sort of perpetual motion is not against the rules ... it's one of Newton's Laws.

    The prohibition is not against perpetual motion, it is against perpetual motion machines - the idea that you can get useful work out of something like this. The maximum amount of energy you can extract from the spinning pencil is the amount of work you did making it spin.

    Donald Simanek has an excellent resource on these things.
    http://www.lhup.edu/~dsimanek/museum/physgal.htm
    ... see the bit about rotations and wheels.
     
  5. Aug 4, 2013 #4
    Hmm. I always thought a constant force was necessary to keep something constantly in circular motion even in absence of friction...
     
  6. Aug 4, 2013 #5

    WannabeNewton

    User Avatar
    Science Advisor

    That's when you have something like a ball tied to a string and need a means of keeping the ball afloat in the air in a circular trajectory by applying a sufficient tension across the string while you stand on the surface of the Earth; this is a case of a controlled circular trajectory about some central point. The OP is instead talking about a situation where you given an initial spin to a pencil in deep isolated space; there are no subsequent external forces at work on the pencil hence nothing to disturb that initial spin.
     
  7. Aug 4, 2013 #6

    A.T.

    User Avatar
    Science Advisor
    Gold Member

    Force is not energy. The centripetal force in uniform circular motion is perpendicular to velocity, so it doesn't do any work on the object.
     
  8. Aug 4, 2013 #7
    I was just saying that there would be no force acting on it after it is released, yet it continues spinning..
     
  9. Aug 4, 2013 #8

    davenn

    User Avatar
    Science Advisor
    Gold Member

    yes.
    reread steamking's post, post #2
    particularly the last sentence :)

    Dave
     
  10. Aug 4, 2013 #9

    CWatters

    User Avatar
    Science Advisor
    Homework Helper

    Perhaps it helps to think of circular motion as having two components, one tangential and the other radial.

    A force is required to produce the radial component but since the radius is constant that force does no work.

    No force is required to maintain the tangential component (there is no air resistance in space).
     
  11. Aug 4, 2013 #10

    Nugatory

    User Avatar

    Staff: Mentor

    There's no net force acting on the entire pencil, so its center of mass isn't moving; the pencil is spinning in place.

    There are forces acting on the ends of the pencil. It's a solid object so it resists stretching, bending, changing shape. Without these forces the tip and eraser end of the pencil would go moving off in different directions; with these centripetal forces they're pulled into circular motion around the center of the pencil.

    However, these forces aren't doing any work because they're acting along the length of the pencil and the pencil is rigid so doesn't change its length.
     
    Last edited: Aug 4, 2013
  12. Aug 4, 2013 #11

    jtbell

    User Avatar

    Staff: Mentor

    The forces between the molecules in the pencil keep those molecules moving in a circular path instead of flying off in a straight line.

    A ball tied to a string attached to a fixed point, and whirling around in a circle, eventually "spins down" because of air resistance (in the earth's atmosphere) and energy losses in the flexing of the string at the attachment point. If you do this on the moon, you eliminate the air resistance, but the flexional losses remain. If you could come up with a way of supporting the string at the center in a way that does not involve any friction or flexing of the string, and do the whole thing in a vacuum, the ball would whirl around forever just like the pencil in space would spin forever.
     
  13. Aug 4, 2013 #12

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    The pencil would continue rotating even if it wasn't rigid (which it isn't; there is no such thing as a truly rigid body).

    The forces that hold the pencil together don't do any work on the pencil because they are internal rather than external forces. Internal forces that are subject to Newton's third law hold the pencil together but they can't change the pencil's total linear or angular momentum.


    It's those internal forces that hold the pencil together that keep the pencil rotating.

    What's been missing from the discussion so far is the concept of angular momentum. Angular momentum is a conserved quantity. An external torque must be applied to the pencil to change its angular momentum. You've ruled out that external torque in the original post, so in a Newtonian world, the pencil must keep on rotating forever to keep that angular momentum constant.
     
  14. Aug 4, 2013 #13

    ehild

    User Avatar
    Homework Helper
    Gold Member

    The spinning pencil does not perform circular motion: but all it points do. A small piece of pencil at distance r from the CM is held at that distance by internal forces acting among the molecules. These internal forces provide the centripetal force to the circular motion of that piece.
    The whole pencil just rotates about its CM, with the angular speed you gave it initially. It will keep its angular momentum forever if no external torque acts on it.
    You can make the pencil perform circular motion in the space by bringing it close to a massive body and give it the appropriate initial velocity for a circular orbit. Gravity would provide the centripetal force .

    ehild
     
  15. Aug 4, 2013 #14
    This discussion has been very informative. I had never before thought about the dynamics of circular motion where the center of mass is stationary.

    I thank each and everyone of you! :)
     
  16. Aug 4, 2013 #15

    A.T.

    User Avatar
    Science Advisor
    Gold Member

    There's no net force acting on the entire pencil, so its center of mass isn't accelerating. Mere movement doesn't require a net force.
     
  17. Aug 4, 2013 #16

    sophiecentaur

    User Avatar
    Science Advisor
    Gold Member

    Whatever forces are acting, no energy is 'consumed' or transferred if there is no movement in the direction of those forces (i.e. the string / pencil gets no longer or shorter). Work done is Force times Distance moved in the direction of the force.
     
  18. Aug 4, 2013 #17

    Nugatory

    User Avatar

    Staff: Mentor

    Yes, of course you're right. This happens sometimes when I post before the second cup of coffee... Jd0g33, I hope you read what I meant to say ("accelerating") and not what I did say ("moving").
     
  19. Aug 7, 2013 #18

    jfizzix

    User Avatar
    Science Advisor
    Gold Member

    It would indeed spin forever, and according to newtonian physics it would keep spinning at the same rate (as is seen with the conservation of angular momentum).

    Things get a little weird when we bring relativity into the picture.

    What happens is that the pencil is spinning (that is, since the velocity of the atoms are not all the same and keep changing in time), the pencil loses energy as gravity waves.

    The rate that energy is being lost depends on how fast the pencil is spinning, so as it slows down, it is also losing energy more slowly. As time stretches on, the pencil never truly stops, but it slows down nearly to zero spin. This doesn't violate any conservation laws, since this angular momentum is transferred to the gravity field.

    The same thing happens in classical electromagnetism, where charged electrons orbiting an oppositely charged nucleus lose energy as electromagnetic waves, and the electrons spiral into the nucleus in about a hundreth of a nanosecond. Of course, that's the classical theory. Quantum mechanicsally, this doesn't happen because the nature of an electron is (apparantly) not to have a well defined position and momentum. There is a minimum energy the electron can have orbiting a nucleus, and this is known as the ground state.

    Compared to the electromagnetic force, gravity is extremely weak, so it would take eons for the pencil to slow down appreciably.
     
  20. Aug 7, 2013 #19
    So you are saying that a rotating object loses energy/momentum through "gravity waves", and a non-rotating object does not?

    I thought that rotational motion is just a special case of linear motion. The difference being that a body in uniform circular motion is undergoing acceleration. So is it the acceleration of rotational motion that is the cause of the energy loss as gravitation waves?

    That would indicate to me that there would be a similar energy loss of a linearly accelerating body due to the gravitational waves that you mention. Is this so?
     
  21. Aug 7, 2013 #20

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    That is right.

    Right.
    More specific, it is the variable quadrupole moment. A perfectly uniform ring could rotate without emitting gravitational waves, for example.

    Right.
     
    Last edited: Aug 7, 2013
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Is uniform circular motion perpetual?
  1. Uniform Circular Motion (Replies: 10)

Loading...