# Linear acceleration and angular acceleration

1. Jun 28, 2010

### thesandalman

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

How do I solve for linear acceleration or angular acceleration without one or the other?
I am given the mass of the object (a yoyo), the inner radius, the outer radius, and Icm (moment of inertia at the center of mass).

Attached in a picture of the problem.

2. Relevant equations

a=alpha *r
alpha=a/r

3. The attempt at a solution

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2. Jun 28, 2010

### rock.freak667

The weight of the yo-yo produced a torque τ and if you did not know, τ = Iα, since you are given 'I', you can get 'α' and hence 'a' using your relevant equations.

3. Jun 28, 2010

### thesandalman

How do you figure out the weight? Also the equation I have in my notes from the lecture, which I just double checked, is torque = I * alpha. Not I * a.

4. Jun 28, 2010

### rock.freak667

α = angular acceleration
a = linear acceleration

Weight is just 'mg'

5. Jun 28, 2010

### thesandalman

I do not know if I am misunderstanding you or what, but that is not the correct answer.

6. Jun 28, 2010

### rock.freak667

What did you have ?

7. Jun 28, 2010

### thesandalman

i have torque is m*g*the outer radius = I* alpha but the answer I got was 651.7 alpha which does not make any sense for a yoyo.

8. Jun 28, 2010

### rock.freak667

Can you post the values? Also the weight does not act there, it acts at through the center. So the weight is right at the start of the inner radius. So you used the wrong radius to get the torque.

9. Jun 28, 2010

### thesandalman

A yoyo with a mass of m = 179 g.
The inner radius of the yoyo is r = 2.60 cm, and the outer radius is R = 3.60 cm
ICM = 9.70×10-5 kgm2

10. Jun 28, 2010

### rock.freak667

11. Jun 28, 2010

### thesandalman

nope.

12. Jun 28, 2010

### rock.freak667

I now read that your inertia is at the center not where it rotates.

You need to use the parallel axis theorem I=Icm +md2 to get the inertia about the point where it rotates and then use the torque.