Question

How do you calculate the velocity of a yo yo with a yo-yo that consists of a disk (or other shape) fixed to an axle that has two strings wrapped around it. As the axle rolls off the strings, the disk and the axle fall as shown in the diagram on the right. (a) If the disk has fallen through a vertical distance of d = 30 cm and the radius of the string and axle is given by r =5.0 mm, how many revolutions has the disk gone through? (b) If the disk is rotating faster and faster with a constant angular acceleration and takes 25 s to fall through the distance d from rest, what is the magnitude of its angular acceleration? (c) What is the magnitude of its angular velocity after the 25 seconds have elapsed? Hint: Use the rotational kinematic equations.

Answer 1

I don't have the image but I'll give you the formalism for a situation illustrated in the figure below:

(a) OBS: I don't know who is r in the text. Check your image and my figure and make the equivalence.

OBS: In fact is a delta(t), but I am using t for simplicity.

Use the first 3 eqs and get: . Replace I_CM and get:

From (1) t will be:

For solving (6) we need omega. Use eqs (3-5) to get omega.

I used a combination of linear with rotational eqs of movement. If you want energetic formalism, you have the eqs (consider the mechanical energies between the strating point-only gravitational potential energy, and final point-rotational and translational energy):

E_i=mgd

Solve the eq: E_i=E_f by using the necessary eqs from the list above, and get the same results.

(b)

From eqs (3) and (1) get:

So, no time and distance required. But it depends if you have both R and r. If not, use the list of eqs from point (a) to solve this point.

(c) See point (a).