For a rolling spherical shell, the ratio of rotational kinetic energy to total kinetic energy is x/5. Find x.

Question

G1 Physics · Accepted Answer

For a spherical shell, I = (2/3)MR² For pure rolling, ω = v/R Rotational kinetic energy: Kᵣₒₜ = (1/2)Iω² = (1/2)(2/3 MR²)(v²/R²) = (1/3)Mv² Translational kinetic energy: Kₜᵣₐₙₛ = (1/2)Mv² Total: Kₜₒₜ = (1/2 + 1/3)Mv² = (5/6)Mv² Thus, Kᵣₒₜ/Kₜₒₜ = (1/3)/(5/6) = 2/5 So x = 2. Final value: 2