Angular Acceleration of Bicycle Wheels

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SUMMARY

The discussion focuses on calculating the angular acceleration of bicycle wheels with a diameter of 109.0 cm as a cyclist accelerates from rest to a speed of 16.3 km/hr in 16.5 seconds. The radius is converted to 0.545 m, and the linear speed is converted to 4.527 m/s. The angular velocity (w) is calculated as 8.3078 rad/s using the formula w = v/r. The angular acceleration (alpha) is determined to be 0.5035 rad/s² using the equation alpha = (wf - wi)/t.

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  • Understanding of angular motion equations
  • Familiarity with unit conversions (e.g., km/hr to m/s)
  • Knowledge of basic physics concepts such as acceleration and velocity
  • Ability to manipulate formulas involving radius and angular velocity
NEXT STEPS
  • Study the relationship between linear and angular motion in physics
  • Learn about the implications of angular acceleration in mechanical systems
  • Explore real-world applications of angular motion in bicycles and vehicles
  • Investigate the effects of wheel diameter on acceleration and performance
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Students studying physics, mechanical engineers, and anyone interested in the dynamics of bicycle motion and angular acceleration calculations.

rustyshackle
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Homework Statement


A wheel has bicycle of diameters 109.0 cm. The bicyclist accelerates from rest with constant acceleration to 16.3 km/hr in 16.5 s. What is the angular acceleration of the wheels?



Homework Equations



w=v/r
alpha= w/t


The Attempt at a Solution



I think I'm doing it right, however, I was hoping someone might check my logic

First I convert diameter 109 cm to radius .545 m and 16.3 km/hr to 4.527 m/s.

I solve for w using linear speed divided by r = 4.527/.545 = 8.3078 rad/s

Solve for alpha using a = (wf-wi)/t = (8.3078-0)/16.5 s = .5035 rad/s^2
 
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Your method seems good to me
 
Thank you :)
 

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