In the velocity example, what wheel diameter was used?

• A. 4 inches
• B. 6 inches
• C. 8 inches
• D. 12 inches

Answer: (B)

Understanding how fast a wheel can push a vehicle starts with how wheel size translates rotation into straight-line motion. The linear velocity at the wheel’s edge comes from the angular speed times the radius: v = ω r. The wheel diameter fixes that radius, so a bigger diameter means a faster edge speed for the same rotation rate (and conversely, a smaller diameter gives a slower edge speed). In the velocity example, a wheel diameter of six inches was used. That sets the radius at three inches and the circumference at six pi inches (about 18.85 inches). For a given angular speed, the linear velocity becomes v = ω × 3 inches (or v = rpm × 18.85 inches / 60, if using rpm). If you chose a different diameter, the velocity would change accordingly, so only the six-inch wheel would yield the numbers shown in the example.