Angular Acceleration of a bicycle

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SUMMARY

The discussion focuses on calculating the angular acceleration of bicycle wheels with a diameter of 0.8 m as a bicyclist accelerates from rest to a speed of 22 km/h (6.11 m/s) in 13.7 seconds. The angular acceleration is derived using the formula ω = ω initial + α * t, where the initial angular velocity (ω initial) is zero. The final angular velocity (ω) is calculated as 15.278 radians per second, leading to an angular acceleration (α) of approximately 1.115 radians per second squared. The discussion also touches on related calculations involving a pulley system.

PREREQUISITES
  • Understanding of angular motion equations, specifically ω = ω initial + α * t
  • Knowledge of unit conversion from km/h to m/s
  • Familiarity with the relationship between linear velocity and angular velocity (v = rω)
  • Basic principles of constant acceleration
NEXT STEPS
  • Study the derivation and application of angular acceleration formulas in rotational dynamics
  • Learn about the conversion techniques between linear and angular measurements
  • Explore the effects of different wheel diameters on angular acceleration
  • Investigate the dynamics of pulley systems and their angular velocity calculations
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the principles of rotational motion and acceleration in bicycles and pulley systems.

maniacp08
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A bicycle has wheels of 0.8 m diameter. The bicyclist accelerates from rest with constant acceleration to 22 km/h in 13.7 s. What is the angular acceleration of the wheels?

relevant equations:
omega = omega initial + alpha * t

22km/h = 6.11m/s

I did 6.11m/s * 13.7s = 83.7207 to get the velocity
then I divided it by .4m to get 209.30175
Im not sure what I should do nextI have another question which is related to the same topic:
A block of 2kg falls with a speed of 3.9m/s from rest to a distance of 2.5m, its acc. is 3.0m/s from a pulley of radius of 8cm.

(b) What is the angular velocity of the pulley at this time?
I used V = R/omega
= 3.9m/s = .08m / omega
omega = .02
This is wrong is my approach wrong?
 
Last edited:
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maniacp08 said:
A bicycle has wheels of 0.8 m diameter. The bicyclist accelerates from rest with constant acceleration to 22 km/h in 13.7 s. What is the angular acceleration of the wheels?

relevant equations:
omega = omega initial + alpha * t

I did 22km/hr * 13.7s = 301.4 km s / hr to get the velocity
Vi = 0
Im not sure what I should do next

First convert km/h to m/s = 1000/3600

v = 22 kmph = 6.1 m/s

w = v/r = 6.1/.4 = 15.278 radians

w = a*t => a = w/t = ... ?
 

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