# 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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###### Problem Details

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 