Angular Acceleration of Wheels: Solve Homework Problem

AI Thread Summary
To solve for the angular acceleration of the cyclist's wheels, the problem states that the wheels make 8.5 revolutions in 4.5 seconds. The correct approach involves converting the revolutions to radians, where 8.5 revolutions equals 53.4 radians. The formula θ = ω₀*t + 1/2*α*t² is used to find angular acceleration (α), but the initial angular velocity (ω₀) must be considered, which is zero since the cyclist starts from rest. The user struggles with the calculations, indicating a misunderstanding of how to apply the formulas correctly. The key to solving the problem lies in accurately determining the angular displacement and applying the equations of motion for rotational dynamics.
Devin Longo
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Homework Statement



A cyclist starts from rest and pedals so that the wheels make 8.5 revolutions in the first 4.5 s. What is the angular acceleration of the wheels (assumed constant)?



Homework Equations



\alpha = \Delta\omega/ \Deltat



The Attempt at a Solution



I converted 8.5 to radians and divided by 4.5. BUT I CANT GET THE RIGHT ANSWER!
 
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Use the formula
θ = ωο*t + 1/2*α*t^2 and find α.
 
So, I do that and I get .839. I kept 8.5 as my theta. It still isn't right. What could I be doing wrong?
 
No. The angular displacement θ = 2*π*n, where n is the number of revolutions per second.
 

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