# Why does this screwdriver roll in a curved trajectory?

I am trying my level best to give this screwdriver a horizontal push only, but it is going in a circular path. I thought of uneven friction due to non-uniform normal reaction...what do you think? I have read up torque a bit, but I dont have a clear understanding of it..does it have anything to do here?

if the above doesn't work: http://www.youtube.com/watch?v=B21BBV0PUXo&feature=youtu.be

• The blunt end of the screwdriver travels a longer distance per revolution than the sharp side. This is similar to how a cone would roll if you were to apply a torque. – Greg May 22 '13 at 16:23
• so it has to do with torque? – Saurabh Raje May 22 '13 at 16:31
• for eg., I thought, well, if I rolled a log of wood, it would go straight and would not turn, but this does turn! – Saurabh Raje May 22 '13 at 16:33
• @Greg, what do u think? – Saurabh Raje May 22 '13 at 16:57
• A log of wood has (roughly) the same diameter at both ends so the distance traveled per revolution is the same. Because the diameters of the two ends of the screwdriver are substantially different, you get a curved path, because the number of revolutions has to be equal for the screwdriver not to twist in on itself – Michiel May 22 '13 at 17:10

## 1 Answer

As both @Greg and @Michiel have stated above, the issue lies with the shape of the screwdriver. The handle side is thicker than the side with the screwdriver blade. The distance traveled by each side during one rotation is equal to its circumference:
$$d=2\pi r$$ For $n$ number of rotations, the equation will look like:
$$d=n 2 \pi r$$ Since every part of the screwdriver is rolling at the same speed (i.e., each part of the screwdriver will have the same number of rotations (n) over a given time) the thicker a given side is the further it will travel relative to a thinner side. That is why the thicker side of the screwdriver travels a longer distance than the thinner side, giving you the circular motion you see.

• so it is maths....not physics? – Saurabh Raje Jun 12 '13 at 14:56
• The formulae are math, applying the formulae to the screwdriver is physics. – NeutronStar Jun 13 '13 at 2:16
• the only physics is when you say that every part is having same no of rotations in given time, isn't it? – Saurabh Raje Jun 13 '13 at 14:47
• I suppose. Physics is a blend of math and the real world though, you can't make physics independent of math. – NeutronStar Jun 13 '13 at 20:36
• yeah...my teacher says physics is applied math. – Saurabh Raje Jun 14 '13 at 15:07