A cyclist is pedaling on his bicycle. If they travelled 18.1 km in 1.0 hours and the diameter of his wheel is 69.3 cm, what was the cyclist's average angular velocity in revolutions per minute (rpm)?

To find the cyclist's average angular velocity in revolutions per minute (rpm), we need to convert the linear velocity to angular velocity.

Step 1: Convert the diameter of the wheel from centimeters to meters.
Given: Diameter = 69.3 cm
To convert centimeters to meters, divide the diameter by 100.
Diameter = 69.3 cm / 100 = 0.693 meters

Step 2: Calculate the circumference of the wheel.
Given: Diameter = 0.693 meters
The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter.
Circumference = π * 0.693 meters

Step 3: Calculate the distance traveled in meters.
Given: Distance = 18.1 km
Since 1 kilometer (km) is equal to 1000 meters (m), we need to convert the distance to meters by multiplying it by 1000.
Distance = 18.1 km * 1000 = 18100 meters

Step 4: Calculate the number of wheel rotations made by the cyclist.
Given:
Distance = 18100 meters
Circumference = π * 0.693 meters
The number of rotations can be found by dividing the distance traveled by the circumference of the wheel.
Number of rotations = Distance / Circumference

Step 5: Convert the number of rotations to revolutions per minute (rpm).
Given: 1 hour = 60 minutes
To convert the number of rotations to rpm, multiply it by 60.
Average angular velocity in rpm = Number of rotations * 60

By following these steps, we can now calculate the cyclist's average angular velocity in revolutions per minute (rpm).

To find the cyclist's average angular velocity in revolutions per minute (rpm), we first need to determine the distance the cyclist traveled along the circumference of the wheel and then convert that into revolutions per minute.

The formula for the circumference of a circle is:
C = π * d

where C is the circumference and d is the diameter.

Given that the diameter of the wheel is 69.3 cm, we can calculate the circumference as follows:
C = π * 69.3 cm

Next, we need to convert the distance traveled by the cyclist, which is given in kilometers, to centimeters since the circumference is in centimeters. To convert kilometers to centimeters, we multiply by 100,000 (since there are 100,000 centimeters in a kilometer).

So, the distance traveled by the cyclist in centimeters is:
Distance = 18.1 km * 100,000 cm/km

Now, we can calculate the number of wheel rotations completed by the cyclist by dividing the distance traveled by the circumference of the wheel:

Number of rotations = Distance / Circumference

Finally, to find the cyclist's average angular velocity in revolutions per minute (rpm), we need to convert the number of rotations into revolutions per minute. Since there are 60 minutes in an hour, we divide the number of rotations by the time in hours and then multiply by 60.

Average angular velocity (in rpm) = Number of rotations / Time * 60

By plugging in the values and performing the calculations, we can find the cyclist's average angular velocity in revolutions per minute (rpm).