If i put a pen on a table in its horizontal position and then i try to move it horizontally by giving it a small push, so that it would fall off a table, i expect it to move horizontally but my pen ( and all other pens too! ) moves diagonally when it starts moving down the table!When i remove the notebook , the pen moves like,its shown in the picture ( if i keep it horizontally also, it gives the same result)-

enter image description here

Why does this happen? Why does it not move horizontally ?

  • $\begingroup$ Some counter questions.. Where do you apply the force? Is the chassis's structure tapered (an exaggeration would be cone)? Other reasons could be non uniform horizontal mass distribution. $\endgroup$ – physicist Jan 4 '16 at 7:34
  • $\begingroup$ Do you know motion Of centre of mass which are uniform or nonuniform $\endgroup$ – Archis Welankar Jan 4 '16 at 7:37
  • $\begingroup$ Your picture is not large enough or clear enough to see what the pen looks like and your statements are incomplete (and possibly wrong :-) ). You say your pen is a cylinder. Does it look like this with r constant at ALL points along its body, or at some points is R different than at others. If r is larger at and point to the left of the right hand end than it is AT the right hand end then you would expect it to move as you have shown. $\endgroup$ – Russell McMahon Jan 4 '16 at 8:06
  • $\begingroup$ @RussellMcMahon My pen is cylindrical if you take out the cone part! $\endgroup$ – Aaryan Dewan Jan 4 '16 at 9:05
  • $\begingroup$ Aaryan - IF it has anything other than a purely cylindrical form when it is rolled then it must roll in a "non-straight" path - for the reasons given by Pela. $\endgroup$ – Russell McMahon Jan 4 '16 at 12:26

Because your pen is not a cylinder, but a portion of a cone. Since it is also rigid, both ends have to complete one cycle of rolling simultaneously. This means that for each cycle, if the narrow and thick ends are separated by the pen's length $L$ and have radii $r_1$ and $r_2$, respectively, they roll $2\pi r_1$ and $2\pi r_2$, respectively. The only way this can be accomplished (without skidding) is for the ends to roll in a cicrcular motion around a common center.

If I haven't miscalculated, then the distance $d$ from the "small" end to this center is $$d = \frac{L}{r_2/r_1–1}$$.

enter image description here

  • $\begingroup$ If i remove the cone part of the pen and then move it in the similar way, then also, it moves in a circular path. I understand what you say , but that does not gives me an answer to the WHY part! Why does it not move horizontally? My pen is a also a cylinder . $\endgroup$ – Aaryan Dewan Jan 4 '16 at 7:51
  • $\begingroup$ Most pens are conical even withour their cap. Even a small difference in radii could be noticable. If you have a caliper and a ruler, you can measure and see if it fits the formula I just added. If not, then I'd go for a misalinged table, or, perhaps, density differences. $\endgroup$ – pela Jan 4 '16 at 8:17
  • $\begingroup$ I am just asking why does it bend? not how but WHY? Why doesn’t it moves horizontally? $\endgroup$ – Aaryan Dewan Jan 4 '16 at 9:08
  • $\begingroup$ @AaryanDewan: I'm sorry, I don't understand the difference. I understand that if your pen is perfectly homogeneous and cylindrical, and your table isn't crooked, and the distance from your system to the nearest black hole can be neglected, then this doesn't answer your question, but otherwise I'm a bit confused. $\endgroup$ – pela Jan 4 '16 at 9:27

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