To find the angular speed of the wheel in radians per second, we need to convert the linear speed of the car into the number of rotations per second.
First, let's convert the car's speed from miles per hour (mph) to inches per second. There are 5280 feet in a mile, 12 inches in a foot, and 3600 seconds in an hour, so the speed in inches per second is calculated as follows:
55 mph * 5280 feet/mile * 12 inches/foot / 3600 seconds/hour = 968 inches/second.
Next, we need to determine the circumference of the wheel. The circumference of a circle is given by the formula 2 * ฯ * radius. In this case, the radius of the wheel is given as 14 inches. So, the circumference of the wheel is:
2 * ฯ * 14 inches = 28ฯ inches.
Now, we can calculate the number of rotations per second by dividing the linear speed of the car (968 inches/second) by the circumference of the wheel (28ฯ inches):
968 inches/second รท (28ฯ inches) = 34.57 rotations/second.
Finally, to find the angular speed in radians per second, we multiply the number of rotations per second by 2ฯ (since there are 2ฯ radians in one revolution):
34.57 rotations/second * 2ฯ radians/rotation = 69.14ฯ radians/second, or approximately 34.57 radians/second.
Therefore, the angular speed of the wheel is approximately 34.57 radians per second.