Question

Question:
Consider a yo-yo as basically a string wound around a cylindrical disk. using terms like
torque, angular momentum, gravity, and conservation. Explain why the yo-yo begins to
roll down, why it will roll back up and lastly explain why it stops and then reverses.
Lastly, in the absence of any frictional loses as the rope unwinds and rewinds, and also
neglecting air resistance, would the yo-yo continue to forever?

Answer 1

Continuation of the above one , the formulas have been given

the yo-yo

Figure 12.6. The yo-yo.

Figure 12.6 shows a schematic drawing of a yo-yo. What is its linear acceleration ?

There are two forces acting on the yo-yo: an upward force equal to the tension in the cord, and the gravitational force. The acceleration of the system depends on these two forces:

The rotational motion of the yo-yo is determined by the torque exerted by the tension T (the torque due to the gravitational force is zero)

The rotational acceleration a is related to the linear acceleration a:

We can now write down the following equations for the tension T

The linear acceleration a can now be calculated

Thus, the yo-yo rolls down the string with a constant acceleration. The acceleration can be made smaller by increasing the rotational inertia and by decreasing the radius of the axle.