How Far Does a Rolling Coin Travel Before Stopping?

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A coin with a diameter of 2.20 cm is dropped on its edge with an initial angular speed of 15.9 rad/s and an angular acceleration of -1.76 rad/s². To determine how far the coin rolls before stopping, the final angular velocity is set to zero to calculate the time taken to stop. Using the formula omega(t) = omega(0) + alpha*t, the time can be derived. Once the stopping time is known, the distance traveled can be calculated. The discussion emphasizes the relationship between angular and linear motion in this context.
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A coin with a diameter of 2.20 cm is dropped on edge onto a horizontal surface. The coin starts out with an initial angular speed of 15.9 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular acceleration of magnitude 1.76 rad/s2, how far does the coin roll before coming to rest?
 
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The formula for calculating angular velocity is similar to the one for linear velocity.
omega(t) = omega(0) + alpha*t
if you set the final angular velocity to zero, you can calculate the amount of time to stop.
 

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