# Problem: A spool floating in space has radius r mass m and moment of inertia about its center I = β mr2. The spool is unwound by a constant force F. If initially the spool is motionless, at some later time what is the ratio of translational kinetic energy to rotational kinetic energy? 1. Ktrans / Krot = (1 + β)2 2. Ktrans / Krot = β2 3. Ktrans / Krot = 1 / β 4. Ktrans / Krot = 1 − β 5. Ktrans / Krot = (1 + β) / β  6. Ktrans / Krot = 1 / β 2 7. Ktrans / Krot = (1 − β)2 8. Ktrans / Krot = 1 + β 9. Ktrans / Krot = β 10. Ktrans / Krot = (1 − β) / β

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A spool floating in space has radius r mass m and moment of inertia about its center I = β mr2. The spool is unwound by a constant force F. If initially the spool is motionless, at some later time what is the ratio of translational kinetic energy to rotational kinetic energy?

1. Ktrans / Krot = (1 + β)2

2. Ktrans / Krot = β2

3. Ktrans / Krot = 1 / β

4. Ktrans / Krot = 1 − β

5. Ktrans / Krot = (1 + β) / β

6. Ktrans / Krot = 1 / β 2

7. Ktrans / Krot = (1 − β)2

8. Ktrans / Krot = 1 + β

9. Ktrans / Krot = β

10. Ktrans / Krot = (1 − β) / β Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Energy of Rolling Motion concept. You can view video lessons to learn Energy of Rolling Motion. Or if you need more Energy of Rolling Motion practice, you can also practice Energy of Rolling Motion practice problems.

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