A rigid body rolls without slipping while attached to a spring and executes small oscillations. Which statements are correct under ideal rolling conditions?
Select all that apply

Question

A rigid body rolls without slipping while attached to a spring and executes small oscillations. Which statements are correct under ideal rolling conditions?

G1 Physics · Accepted Answer

For rolling, v = RΩ. Therefore, K = ½Mv²+½I(v²/R²) = ½[M+I/R²]v². Hence the rotational part adds to the effective inertia. For the centre spring, Mₑ = M+I/R². For a material point initially at the top, translational and rotational contributions to its horizontal displacement add, giving approximately 2x for small motion. For a solid sphere, I = 2MR²/5, so Mₑ = 7M/5 and ω² = k/(7M/5) = 5k/(7M). Therefore all four statements are correct.