Final answer:
To determine the rotation rate of the tire in rpm, the tire's circumference is calculated using its diameter, and this value is then used to calculate the number of revolutions per second based on the car's speed, which is then converted to rpm, resulting in 1125 rpm.
Step-by-step explanation:
To calculate the tire's rotation rate in revolutions per minute (rpm), we need to figure out how many revolutions the tire makes in a single second and then convert that to minutes. First, we find the tire's circumference using the diameter given. The circumference (C) of a tire is π times the diameter (D), hence C = π × 46.6 cm. Converting this to meters gives us C = 0.466 meters since 1 cm = 0.01 m. Now, if the car travels at 27.4 m/s, in one second it covers 27.4 meters, which is equivalent to 27.4 / C revolutions. We would then multiply this value by 60 to convert seconds to minutes for the rpm.
Let’s calculate: First, find the circumference C = 3.14159 × 0.466 m = 1.461 m. Next, calculate the number of revolutions per second: 27.4 m/s ÷ 1.461 m/rev = 18.75 rev/s. Finally, convert to rpm: 18.75 rev/s × 60 s/min = 1125 rpm.