A solid sphere rolls without slipping. The ratio of its angular momentum about its rotation axis to its total kinetic energy is π:22. Find its angular speed in rad s⁻¹.

Question

G1 Physics · Accepted Answer

For a solid sphere, I = (2/5)MR² Angular momentum: L = Iω = (2/5)MR²ω Total kinetic energy for rolling: E = (1/2)Mv² + (1/2)Iω² With v=ωR: E = (1/2)Mω²R² + (1/5)Mω²R² = (7/10)Mω²R² Therefore, L/E = [(2/5)MR²ω]/[(7/10)Mω²R²] = 4/(7ω) Given: L/E = π/22 So, 4/(7ω) = π/22 ω = 88/(7π) Using π = 22/7: ω = 4 rad s⁻¹ Final value: 4