Rotational Kinetic Energy
KE_rot = ½Iω² — compare with translational KE for rolling objects.
Key Notes
Rotational kinetic energy: K_rot = ½Iω². Direct analog of K_trans = ½mv².
Total KE of a rolling body = K_trans + K_rot = ½Mv² + ½Iω². With v = rω (rolling condition).
For a rolling solid sphere: K_total = ½Mv² + ½·(2MR²/5)·(v/R)² = (7/10)Mv². So 71% translation, 29% rotation.
Disk rolling: K_total = (3/4)Mv². Hollow sphere: (5/6)Mv². Ring: Mv² (50/50 split).
Energy stored in a flywheel: K = ½Iω². Large I and large ω ⇒ huge storage. Used in regenerative braking.
Work done by torque: W = ∫τ·dθ = ΔK_rot.
Power delivered to rotating body: P = τ·ω.
Rotation kinetic energy is real KE — has the same units (J) and converts to/from translational KE in rolling.
Formulas
Rotational KE
Direct analog of ½mv².
Total KE (rolling)
Substitute v = ωR for rolling without slipping.
Work-energy (rotation)
Torque does work; changes K_rot.
Rotational power
Direct analog of P = Fv.
Important Points
K_rot is REAL energy — comparable to and convertible with translational KE.
Rolling adds rotational KE — a rolling solid sphere has 1.4× the KE of a sliding block at same v.
Why a sliding block reaches the bottom of a ramp BEFORE a rolling sphere: rolling sphere stores energy in rotation, leaving less for translation.
Hollow vs solid: hollow ring (I = MR²) stores MORE rotational energy than solid disk (½MR²) at same ω.
Flywheel energy storage: industrial-scale flywheels can store MJ. Important for grid stability.
Common pitfall: forgetting K_rot when analyzing rolling motion.
Rotational Kinetic Energy notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.