Yo-yo problem - rotational motion

[Physics197]

Homework Statement

consider a yo-yo with R = 3.3 cm, r = 0.3 cm, and mass m = 84 g.

What is the speed of the yo-yo after it has fallen a distance h = 1.20 m?

What is the tension in the string while the yo-yo falls?

What is the magnitude of the acceleration of the centre of mass as the yo-yo falls?

Homework Equations

L = Iw
I = 0.5MR^2
KEr = 0.5Iw^2
Tnet = Ia

The Attempt at a Solution

change h into rotational displacement, not sure where to go or if that's even right.

can anyone give me direction?

 

[Physics197]

would you solve this using conversation of energy?

 

[Delphi51]

Yes, I would use energy for the first part. You have both rotational and translational energy and they are related by v = rω. The r = 0.3 cm must be the radius of the center "axel" that the string unwraps from.

If you don't put in the h = 1.2 too soon, you'll have the speed as a function of h. Perhaps you can differentiate that with respect to time and get something you can use to find the acceleration.

 

[Physics197]

what would the moment of inertia be? 0.5mr^2, would you use the large or small radius?

would the height be 1.2 m? for PE

 

[Delphi51]

Yes, the large radius for moment of inertia.
Yes, the initial height is 1.2 m.