what is the angular velocity in radians per second of a bicycle tire of diameter 70 cm, when the bike is traveling at 30km/h?
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To find the angular velocity in radians per second of a bicycle tire, we need to use the formula:
Angular Velocity (in radians per second) = Linear Velocity (in meters per second) / Radius of the bicycle tire (in meters)
First, let's convert the diameter of the tire to the radius:
Radius = Diameter / 2
Given that the diameter of the tire is 70 cm, the radius would be:
Radius = 70 cm / 2 = 35 cm
Now, we need to convert the radius from centimeters to meters:
Radius = 35 cm * 1 m / 100 cm = 0.35 m
Next, let's convert the bike's speed from km/h to m/s:
Speed (in m/s) = Speed (in km/h) * 1000 m / 3600 s
Given that the bike is traveling at 30 km/h, the speed in m/s would be:
Speed (in m/s) = 30 km/h * 1000 m / 3600 s = 8.33 m/s
Now, we can calculate the angular velocity:
Angular Velocity (in radians per second) = Speed (in m/s) / Radius
Using the values we have:
Angular Velocity (in radians per second) = 8.33 m/s / 0.35 m = 23.8 radians per second
Therefore, the angular velocity of a bicycle tire with a diameter of 70 cm, when the bike is traveling at 30 km/h, is approximately 23.8 radians per second.