Step‑by‑step example: 1. **Given**: Radius r = 0.5 m, initial angular velocity ω₀ = 0 (starts from rest), time t = 4 s, angular displacement θ = 8π rad. 2. **Find angular acceleration α** using θ = ω₀ t + ½ α t². - Plug in values: 8π = 0·4 + ½ α (4)². - Simplify: 8π = ½ α · 16 → 8π = 8α → α = π rad/s². 3. **Find final angular velocity ω** using ω = ω₀ + α t. - ω = 0 + π·4 = 4π rad/s. 4. **Find linear speed v** of a point on the rim using v = r ω. - v = 0.5 m · 4π rad/s = 2π m/s. 5. **Result**: Angular acceleration α = π rad/s², final angular velocity ω = 4π rad/s, linear speed v = 2π m/s. So the wheel speeds up steadily, turning 8π radians in 4 seconds, ending with a linear speed of about 6.28 m/s on its outer edge.