Coin rolling with constant deceleration, how much time to go 1.6m

AI Thread Summary
The discussion focuses on calculating the time a coin rolls before falling off a table, given its initial and final angular velocities and the distance traveled. The initial angular velocity is 3.4 rad/s, and it decelerates to 1.2 rad/s over a distance of 1.6m. A key point is the need to convert the number of rotations into radians for accurate calculations. The attempted solution incorrectly used the number of rotations instead of the angular displacement in radians. The correct approach involves using the formula for angular displacement to find the time taken for the coin to roll off the table.
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Homework Statement



A coin is rolled without slipping on a table top in a straight line. It starts rolling at 3.4 rad/s and slows down at a constant angular acceleration. It is rolling at 1.2 rad/s when it falls off the table edge. If the radius of the coin is 0.011m, and the edge of the table is 1.6m from where the coin started, for how much time did the coin roll?

Homework Equations



Wi = 3.4rad/s
Wf = 1.2rad/s
\DeltaX = 1.6m
radius = 0.011m

\theta = \frac{1}{2}(Wf + Wi)* t
Wf = Wi) + \alpha*t



The Attempt at a Solution




2*pi* r = 0.691
1.6m / 0.691 = 23.15 full rotations

23.15 = 1/2 (Wf + Wi)*t
23.15 = 1/2 (1.2 + 3.4)*t
...
t = 10.07sec

That didn't work. I assume it has something to do with calculating how many rotations, or the actual angle displacement.
 
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Well, it looks like you calculated your number of rotations right, but I noticed you plugged that directly into your equation. The value theta represents the radians that are displaced, not the number of revolutions. You first need to convert your revolutions to radians and then use that value for theta.
 

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