Final answer:
To calculate the angular speed of a bicycle's wheel, you first convert the linear speed to inches per minute, then divide by the wheel's radius to find revolutions per minute and finally multiply by 2π to get radians per minute. The angular speed is approximately 8282.4 rad/min, and the wheel makes 660 revolutions per minute.
Step-by-step explanation:
To find the angular speed of the wheels in rad/min and the number of revolutions per minute the wheels make, we need to consider the relationship between linear and angular velocities. The formula v = r⋅ω connects linear speed (v), radius (r), and angular speed (ω).
Firstly, we convert the linear speed from mi/h to inches/min:
Next, we find the bicycle wheel radius in inches (since diameter = 24 inches, radius = diameter/2):
Now we calculate the angular speed ω using the formula:
To calculate the number of revolutions per minute: