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

[IAmPat]

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
[tex]\Delta[/tex]X = 1.6m
radius = 0.011m

[tex]\theta[/tex] = [tex]\frac{1}{2}[/tex](W_f + W_i)* t
W_f = W_i) + [tex]\alpha[/tex]*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.

 

[MacDougal87]

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.