How Far Does a Rolling Coin Travel Before Stopping?

AI Thread Summary
To determine how far a rolling coin travels before stopping, the initial angular speed of 13.4 rad/s and angular acceleration of -2.03 rad/s² are used in the equation wf² = wi² + 2a(dTheta). The calculated angular displacement is 44.2 radians, which needs to be converted to linear distance. The diameter of 1.50 cm is relevant for calculating the circumference, as the distance traveled can be found using the formula distance = circumference × (dTheta / 2π). Ultimately, understanding the relationship between angular displacement and linear distance is crucial for solving the problem.
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A coin with a diameter of 1.50 cm is dropped on edge onto a horizontal surface. The coin starts out with an initial angular speed of 13.4 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular acceleration of magnitude 2.03 rad/s2, how far does the coin roll before coming to rest?


I know that wf^2 = wi^2 + 2a(dTheta) should be used, and I find theta to be 44.2 but the 44.2 is in rads, so how do i translate this into ms? What does the 1.50 diameter have to do with this problem?
 
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Leid_X09 said:
A coin with a diameter of 1.50 cm is dropped on edge onto a horizontal surface. The coin starts out with an initial angular speed of 13.4 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular acceleration of magnitude 2.03 rad/s2, how far does the coin roll before coming to rest?


I know that wf^2 = wi^2 + 2a(dTheta) should be used, and I find theta to be 44.2 but the 44.2 is in rads, so how do i translate this into ms? What does the 1.50 diameter have to do with this problem?

How many radians to one revolution?

What distance is that? Maybe think circumference plays a part?
 

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