Vertical Circle — EnergyHardQuestion 30632
Question
A ball moving in a vertical circle (radius r) has speed v₀ at the bottom. At angle θ from the bottom, the speed is:
- Av₀ − gr(1−cosθ)
- B√(v₀²−2gr(1−cosθ))Correct
- C√(v₀²−2gr)
- Dv₀√cosθ
Correct answer
√(v₀²−2gr(1−cosθ))
Explanation
Height gained = r − r cosθ = r(1−cosθ). Energy conservation: ½mv² = ½mv₀² − mg×r(1−cosθ) → v = √(v₀²−2gr(1−cosθ)).