How Do You Calculate Angular Velocity for a Bicycle Tire?

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SUMMARY

The calculation of angular velocity for a bicycle tire traveling at 18 km/h with a diameter of 70 cm results in an angular velocity of 4.6π rad/s. The process involves converting the speed from km/h to cm/s, calculating the circumference of the tire using the formula C = 2πr, and then determining the number of rotations per second by dividing the speed by the circumference. The final step multiplies the rotations per second by 2π to convert to radians per second, confirming the accuracy of the method used.

PREREQUISITES
  • Understanding of angular velocity calculations
  • Familiarity with the relationship between linear speed and rotational motion
  • Knowledge of basic geometry, specifically circumference calculation
  • Ability to convert units of measurement (e.g., km/h to cm/s)
NEXT STEPS
  • Study the concept of angular velocity in rotational dynamics
  • Learn about unit conversions in physics, particularly speed and distance
  • Explore the relationship between linear and angular motion
  • Investigate real-world applications of angular velocity in cycling and other sports
USEFUL FOR

Physics students, mechanical engineers, cycling enthusiasts, and anyone interested in the dynamics of rotational motion.

Imperil
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A bicycle travels at 18 km/h. The tires on the bicycle are 70 cm in diameter. Determine the angular velocity in rad/s.

My work:

18 km/h = 1800000 cm / 60^2 s = 500 cm / s
C = 2Pi(35 cm) = 70Pi cm
500 cm / 70Pi cm = 2.3 rotations / s
2.3 x 2Pi = 4.6Pi rad/sec

First I determine the speed in cm / s, then the circumference of the tire, divide the speed by circumference to get number of rotations per second, then multiply the number of rotations by 2PI which then gives me 4.6PI rad/sec

Am I correct? Or have I done something wrong?
 
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I didn't check your arithmetic but your reasoning is correct.
 

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