Final answer:
The angular velocity of the car's tire is 29.33 rad/s, and it rotates at a rate of 278.73 revolutions per minute (RPM).
Step-by-step explanation:
The angular velocity of a car's tire can be calculated using the formula:
angular velocity (in rad/s) = linear velocity (in m/s) / tire radius (in meters)
In this case, the car is traveling at 35 mph, which is equivalent to 15.65 m/s. The tire diameter is 21 inches, which is 0.5334 meters. Using the formula, we can calculate the angular velocity:
angular velocity = 15.65 m/s / 0.5334 m = 29.33 rad/s
To convert this to revolutions per minute (RPM), we can use the conversion factor:
1 revolution = 2π radians
angular velocity in RPM = (29.33 rad/s * 1 revolution / 2π radians) * 60 seconds
angular velocity in RPM = 278.73 RPM