Tilting ball arm physics

A tilting arm with room for 6 balls

Properties affecting behaviour of the tilting arm

  • Position of pivot point S,vertically and horisontally, in relation to arm and balls.
  • Position of centre of mass M (of arm and balls combined), vertically and horisontally in relation to pivot point.
  • Mass of balls in relation to mass of arm.
  • How the mass is distributed, close to or far from the centre of mass.
 

Some observations

  1. If the centre of mass M is to the right of the pivot point S, the arm tilts to the right. 

  2. If M is to the left of S, the arm tilts to the left. 
  3. Adding a ball or other mass to the left of M moves M slightly to the left.

  4. Adding a ball or other mass to the right of M moves M slightly to the right. 
  5. In this kind of system M should normally be above S. Tilting the arm to the left will cause M to move slightly to the left. Imagine M high above S to see this. If tilting moves M to the other side of S, the arm will be stable in both positions.

  6.  
  7. With 0 to 5 balls on the arm, and the arm tilted to the right, M should be to the right of S.
  8. Adding the 6th ball should move M to the left side of S and start tilting.
  9. With the arm tilted to the right and empty except for the first ball arriving on the left end, M should still be to the right of S to avoid tilting. If this cannot be achieved, the arm may still operate correctly if the ball rolls quickly to the right end.

  10.  
  11. When the arm is tilted to the left, and the balls roll of, M should stay to the left of S even when only one ball is left on the left end of the arm. Otherwise the arm may tilt back to the right before the last ball has left. 
 

Practical considerations

  1. The 7th point above is difficult to achieve on arms where all balls are to the left of the pivot point. The trick is to ensure that M moves enough to the left when tilting. I use three different means to achieve this:
    1. On the upper arm of the clock at Vitensenteret I have added an extra weight above the balls to move M upwards and make M larger in relation to the weight of the balls.
    2. On the lowest arm of my clock at home I have placed the pivot point lower than on the other arms.
    3. On the lowest arm of my clock at home I have also added an extra (brown) ball at the right end. It helps to move M to the left when the arm tilts.
  2. If the arm is too heavy in relation to the balls, it will tilt slowly. This can cause the balls to roll with different speed, causing erratic behaviour.
  3. If the track is too wide, the balls may roll slowly or not at all. See the other theory page for explanation.
  4. For visual appearance I have chosen to make all arms of equal length and with pivot point in the same place horisontally. This makes adjustment of the arms more complex, but it is still possible to construct a working clock.

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Last modified 15.05.98