Final answer:
To maintain a speed of 66 km/h, the motorcycle wheel with a radius of 35 cm must rotate at approximately 500.52 RPM, not the 250 RPM stated in the question.
Step-by-step explanation:
To calculate how many revolutions per minute (RPM) a motorcycle wheel must make to maintain a speed of 66 km/h, let's first convert speeds to a consistent unit. We know that 1 km = 1000 meters and 1 hour = 3600 seconds; therefore, 66 km/h can be converted to meters per second (m/s) as follows: (66 km/h) * (1000 m/km) / (3600 s/h) = 18.333 m/s.
Next, we need to calculate the distance traveled in one revolution of a wheel. This is the circumference of the wheel, which is given by 2 * π * radius. Since the radius is 35 cm, or 0.35 meters, the circumference is 2 * π * 0.35 m = 2.199 m per revolution.
To find the RPM, we divide the linear speed by the circumference of the wheel and convert that to minutes:
(18.333 m/s) / (2.199 m/rev) = 8.342 rev/s. Then, we multiply by 60 seconds per minute to get RPM: 8.342 rev/s * 60 s/min = 500.52 RPM. However, the student is seeking a 250 RPM, which does not match the calculated value.