# Yo-Yo conservation of energy

1. Aug 10, 2013

### postfan

1. The problem statement, all variables and given/known data

A yo-yo has mass 0.8 kg and rotational inertia 0.12 kg m2 measured about an axis perpendicular to the screen and passing through its center of mass. A light thin string is wrapped around the central part of the yo-yo that has radius 0.03 m. The string is attached to the ceiling as shown. The yo-yo is released from rest and begins to descend as the string unwraps.

Use conservation of energy to find the linear speed of the yo-yo by the time it descended a distance 0.8 m. Use g = 9.8 m/s2.

2. Relevant equations

3. The attempt at a solution

Used conservation of energy :mgh=.5mv^2+.5Iw. w=v^2/r^2. v=3.74.

What am I doing wrong?

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Last edited: Aug 10, 2013
2. Aug 10, 2013

### Delphi51

Is the question to find the vertical velocity? At what distance fallen? You really should quote the entire question exactly as it is given to you. If you have, the answer cannot be found.
Which radius did you use in w=v/r ?

Last edited: Aug 10, 2013
3. Aug 10, 2013

### Simon Bridge

This is quite a common HS problem, it is reasonable to put I as about the center of rotation here:
You need to explain your reasoning here and show the rest of your working for this to make any sense.
The attached diagram does not belong to this problem either - it's missing at least one force.
Then - there is no question in the problem statement.

The basic approach - that grav PE lost is stored as linear motion and in the rotation of the yoyo - is correct.

4. Aug 10, 2013

### postfan

Well m=.8, g=9.8, h=.8 w=v/r. So I substituted these values in the above equation and got 3.74, which I know is wrong. So what am I doing wrong?

5. Aug 11, 2013

### postfan

I resolved it and got the same answer 3.74, but it is wrong, can anyone please tell me why that's so?

6. Aug 11, 2013

### Staff: Mentor

Double check your arithmetic.

7. Aug 11, 2013

### postfan

Is the answer 3.69?

8. Aug 11, 2013

### pgardn

What is the radius of the entire yo-yo?

The whole thing has rotational K.

9. Aug 11, 2013

### postfan

The radius is .03.

10. Aug 11, 2013

### pgardn

That is the inner radius where the string is tied according to the diagram.

11. Aug 11, 2013

### postfan

Can we say that the radius of the entire yo-yo is R?

12. Aug 11, 2013

### pgardn

You are given the rotational inertia. Since the problem does not state what type of extended mass the yo yo is we need the radius. Are you looking at the correct diagram?

13. Aug 11, 2013

### postfan

The diagram is correct, and the problem doesn't give us the radius of the entire yo-yo.

14. Aug 11, 2013

### rcgldr

The problem states the rotational inertia of the entire yo-yo so use that. From the first post in thread:

15. Aug 11, 2013

### Staff: Mentor

Why would you need that?

16. Aug 11, 2013

### postfan

Wait , do I need to find the radius or not?

17. Aug 11, 2013

### pgardn

I wast thinking v^2 / r^2 part?

But now I think I can find omega...

18. Aug 11, 2013

### postfan

I'm really confused , do I need to find the radius or not?

19. Aug 11, 2013

### rcgldr

The problem states that the yo-yo has rotational inertia I = 0.12 kg m^2. There's no need to find the radius of the yo-yo, and that wouldn't help unless you knew how the mass in the yo-yo was distributed.

There's also a typo in your equation (you left out the ^2 for w^2), which should be:

m g h = .5 m v^2 + .5 I w^2

20. Aug 11, 2013

### postfan

So do I just substitute and solve?