Problem: As seen from above in the image, a string is wrapped around the edge of a uniform cylinder of radius R and mass M which is initially resting motionless on a frictionless table. The end of the string is pulled with a force of F over a distance l. If the linear speed of the cylinder is found to be v after pulling this distance, what is the angular speed of the cylinder? (Note that v ≠ ωR in this case.) 1. ω = √ (4 / MR 2) (Fl - 1/2Mv 2) 2. ω = √ (4 / 3MR 2) FR 3. ω = √ (2 / MR 2) (FR - 1/2Mv 2) 4. ω = √ (1 / MR 2) Fl 5. ω = √ (2 / 3MR 2) FR 6. ω = √ (4 / MR 2) (FR - 1/2Mv 2) 7. ω = √ (2 / MR 2) (Fl - 1/2Mv 2) 8. ω = √ (2 / 3MR 2) Fl 9. ω = √ (4 / 3MR 2) Fl 10. ω = √ (1 / MR 2) FR

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Problem Details

As seen from above in the image, a string is wrapped around the edge of a uniform cylinder of radius R and mass M which is initially resting motionless on a frictionless table. The end of the string is pulled with a force of F over a distance l. If the linear speed of the cylinder is found to be v after pulling this distance, what is the angular speed of the cylinder? (Note that v ≠ ωR in this case.)

1. ω = √ (4 / MR 2) (Fl - 1/2Mv 2)

2. ω = √ (4 / 3MR 2) FR

3. ω = √ (2 / MR 2) (FR - 1/2Mv 2)

4. ω = √ (1 / MR 2) Fl

5. ω = √ (2 / 3MR 2) FR

6. ω = √ (4 / MR 2) (FR - 1/2Mv 2)

7. ω = √ (2 / MR 2) (Fl - 1/2Mv 2)

8. ω = √ (2 / 3MR 2) Fl

9. ω = √ (4 / 3MR 2) Fl

10. ω = √ (1 / MR 2) FR

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