Final answer:
To find out how many times per second a car wheel rotates at 65 mph, calculate the tire's circumference and divide the car's speed, converted to inches per second, by this circumference.
Step-by-step explanation:
To calculate how many times per second a car wheel rotates when the car is traveling at 65 miles per hour, we can use the concept of angular velocity in physics. First, we need to know the circumference of the car's tire, which can be found using the equation C = 2πr, where r is the radius of the tire. Once we have the circumference, we can calculate the number of rotations by dividing the car's speed by the tire's circumference. Since we're interested in the number of rotations per second, we'll convert the car's speed from miles per hour to inches per second (as the tire's dimensions are typically in inches) and then divide by the circumference, also in inches.
Let's assume a typical car tire diameter of about 25 inches, giving a radius of 12.5 inches. The circumference C would then be 2π × 12.5 inches. The car's speed in inches per second is 65 miles per hour × 5,280 feet per mile × 12 inches per foot / 3,600 seconds per hour. Dividing this speed by the circumference of the tire gives us the rotation rate in revolutions per second.