- #1

Ryker

- 1,086

- 2

## Homework Statement

The yo-yo is made of two wheels, connected by a short beam (the cross-section of the beam looks like the letter "H"), around which wire is wrapped up. Let the yo-yo be stationary on a desk. What is the angle ß in relation to the said desk (see picture) that we must gently pull the wire so as not to cause the yo-yo to roll?

The picture is really small, so to give a legend of sorts: "r" is used for the diameter of the inner circle, "R" for the bigger one, "ß" for the angle and "F" for the force with which we pull the wire.

## Homework Equations

## The Attempt at a Solution

I was really lost on this one, until I looked up the solution and tried to make sense of it. The following is the best I can come up with.

So there's three forces acting on the yo-yo, which is the force with which we're pulling the wire, the yo-yo's weight and the force of the desk (comprised of static friction and a force opposing the weight of the yo-yo). Since the yo-yo is not moving, they, along with the torque they cause, must equal zero.

So we first look at our force "F", which can be seen as a result of two components, one being parallel to the desk and the other perpendicular to it. For that we sketch a triangle or a rectangle. The force parallel to the desk points in the opposite direction to the force of static friction and must therefore cause equal torque. Said torque must be in linear relation to the diameter of the inner circle "r", because that's where the force "F" has its hold. The force "F" itself, too, must be in such a relation to the total force of the desk to cause the same torque. Therefore, as the desk touches the yo-yo at outer rim of a circle with the diameter "R", the force "F" is in linear relation to "R".

Looking again at the triangle (or rectangle) again we find that the solution to the problem is:

[tex]\cos (\beta) = \frac{r}{R}[/tex]

I don't know, seems a bit shaky to me, so that's why I thought maybe someone can look at the problem and see if I went into the right direction with my thinking.