Rotational Motion: Finding Angle of Chalk Line on Rotating Bicycle Wheel

AI Thread Summary
The problem involves calculating the angle a chalk line on a rotating bicycle wheel makes with its original direction after a given time, using angular speed and acceleration. The initial angular speed is 2.84 rad/s, and the angular acceleration is 1.75 rad/s². The attempted solution using the equation Δθ = ωt + (1/2)(ang. accn)t² yields a result of 7.77 rad, but the user is unsure about the correctness of this calculation. There is confusion regarding the application of angular acceleration and whether adjustments like subtracting 2π are necessary for the final answer. Clarification on these points is sought to resolve the issue.
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Homework Statement


A rotating bicycle wheel has an angular speed of 2.84 rad/s at some instant of time. It is then given an angular acceleration of 1.75 rad/s2. A chalk line drawn on the wheel is horizontal at t = 0. What angle does this line make with its original direction at t = 1.77 s?

Homework Equations



The rotational kinematics equations.

The Attempt at a Solution



Using the equation:

Δθ = ωt + (1/2)(ang. accn)t2

= (2.84)(1.77) + 0.5 (1.75)(1.77)^2
= 7.77rad

I can't get it right. I have a feeling I have to use the angular acceleration to change the angular velocity, but I can't figure out how to do this. It's probably something really silly so if someone could point out what I'm doing wrong it would be much appreciated.
 
Last edited:
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Angular acceleration is 1.75, not 1.62
 
ahsanxr said:
Angular acceleration is 1.75, not 1.62

Sorry, typo. Fixed now. Answer is still wrong.
 
Anybody?
 
Maybe you should subtract 2pi from the answer?
 

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