How fast is a bicycle traveling in feet per second if a wheel has a 21-in. diameter and the angular speed of the wheel is 33 radians per second? The speed of the bicycle is the same as the linear speed of a wheel.
A 21 inch diameter wheel had a radius of R = 10.5 cm. The speed in inches per second is R*(angular speed) = 346.5 inch/s = 28.9 ft/s.
To find the linear speed of the bicycle, we can use the formula:
Linear Speed (v) = Angular Speed (ω) × Radius (r)
First, let's convert the diameter of the wheel from inches to feet. Since 1 foot is equal to 12 inches, the diameter of the wheel in feet is:
Diameter = 21 inches = 21/12 feet = 1.75 feet
Next, we need to find the radius of the wheel, which is half of the diameter:
Radius (r) = Diameter/2 = 1.75 feet/2 = 0.875 feet
Now that we have the radius of the wheel, we can substitute this value and the given angular speed into the formula:
Linear Speed (v) = 33 radians/second × 0.875 feet
Multiply the angular speed by the radius to get the linear speed:
v = 33 × 0.875 = 28.875 feet/second
Therefore, the bicycle is traveling at a speed of approximately 28.875 feet per second.