A solid sphere of mass 2 kg and radius 0.1 m rolls without slipping at v_cm = 3 m/s. Find (a) its angular velocity and (b) its total kinetic energy. Step 1: Rolling without slipping gives ω = v_cm / R = 3 / 0.1 = 30 rad/s. Step 2: For a solid sphere, I = (2/5)mR² = 0.4 × 2 × 0.01 = 0.008 kg·m². Step 3: Translational KE = ½mv_cm² = ½ × 2 × 9 = 9 J. Step 4: Rotational KE = ½Iω² = ½ × 0.008 × 900 = 3.6 J. Step 5: Total KE = 9 + 3.6 = 12.6 J. Answer: (a) 30 rad/s, (b) 12.6 J. Notice the spin carries a full 3.6 J — nearly 30% of the total energy is hidden in rotation.