Given a motor shaft speed of 150 rpm, a 6 inch diameter wheel and 75% efficiency, what is the linear velocity of the robot?

• A. 2.9 ft/s
• B. 3.5 ft/s
• C. 4.2 ft/s
• D. 1.5 ft/s

Answer: (A)

Rotational speed becomes linear speed through the wheel’s circumference, with efficiency reducing the effective output.

A wheel with 6 inches diameter has a circumference of π × 6 = 6π inches ≈ 18.85 inches. The motor speed is 150 rpm, which is 150/60 = 2.5 revolutions per second. So the wheel covers 2.5 × 18.85 ≈ 47.12 inches each second before losses. That’s about 47.12 / 12 ≈ 3.93 feet per second.

Accounting for 75% efficiency, the actual (forward) speed is 0.75 × 3.93 ≈ 2.95 ft/s, which is about 2.9 ft/s.