bike tires are 22 inches in diameter and has an angular speed of 5 miles per second, how fast is the bike traveling in mph

Angular velocity is usually given in rad/s., deg./s, or rev/min. So please

check your INFO.

To find out how fast the bike is traveling in mph, we need to use the relationship between the angular speed of the tires and the linear speed of the bike.

First, we need to convert the angular speed from miles per second to radians per second. Since one revolution is equal to 2π radians, we can use the conversion factor:

1 revolution = 2π radians.

The linear distance traveled by a point on the tire in one revolution is equal to the circumference of the tire. The formula for the circumference of a circle is:

Circumference = 2π × radius.

Given that the diameter of the tire is 22 inches, the radius would be half of that, which is 11 inches. Converting the radius to feet (1 foot = 12 inches):

Radius = 11 inches = 11/12 feet.

Now, we can calculate the circumference of the tire:

Circumference = 2π × 11/12 feet.

Next, to find the linear speed of the bike, we multiply the circumference of the tire by the angular speed. The formula is:

Linear speed = Angular speed × Circumference.

Finally, we need to convert the linear speed from feet per second to miles per hour. Since 1 mile = 5280 feet and 1 hour = 3600 seconds, we can use the conversion factors:

1 mile/5280 feet = 1/5280 miles/feet,
1 hour/3600 seconds = 1/3600 hours/seconds.

Multiplying the linear speed by these conversion factors will give us the answer in mph.

Now, let's calculate the linear speed of the bike in mph:

1. Convert angular speed from miles per second to radians per second:
Angular speed = 5 miles/second × 2π radians/1 revolution.

2. Calculate the circumference of the tire in feet:
Circumference = 2π × 11/12 feet.

3. Calculate the linear speed of the bike in feet per second:
Linear speed = Angular speed × Circumference.

4. Convert the linear speed from feet per second to miles per hour:
Linear speed in mph = Linear speed in feet/second × 1/5280 miles/feet × 3600 seconds/hour.

By following these steps and performing the calculations, you will be able to determine the speed of the bike in mph based on the given information.