A stationary bicycle wheel of radius R is mounted in the vertical plane on a horizontal low friction axle. Initially the wheel is not rotating. The wheel has mass M, all concentrated in the rim (spokes have negligible mass). A lump of clay with mass m falls and sticks to the outer edge of the wheel at an angle θ as shown in the figure. Just before impact the clay has a speed v. Just after impact, what is the magnitude of the angular velocity of the wheel?
1. mvcosθ / MR
2. mv / (m + M)R
3. mv / MR
4. mvcosθ / (m + M)R
5. mvsinθ / (m + M)R
6. mv / (m + M)R 2
7. Mv / mR
8. Mvsinθ / mR
9. mv / MR 2
10. mvsinθ / MR
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