Easy angular velocity question

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The problem involves a solid disk with a radius of 1.4 cm and 2.0 m of string, which is unwound by a constant force over 7.3 seconds. The correct final angular velocity of the disk is 39.1 rad/s, but the user calculated 19.6 rad/s by determining linear velocity first. The confusion arises from the interpretation of constant force, which implies constant acceleration rather than constant velocity. To find the correct angular velocity, the user needs to account for the acceleration caused by the constant force acting on the disk. Understanding the relationship between linear and angular motion is crucial for solving this problem correctly.
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Homework Statement



A solid disk with a radius of 1.4cm is a rest. The disk has 2.0m of string wound on to its circumference. The string is pulled off the disk by a constant force in a time of 7.3s. What is the final angular velocity of this disk?


Homework Equations



v = r*ω

The Attempt at a Solution



The correct answer is 39.1 rad/s but I keep getting half of that (19.6 rad/sec).

Since ω = v/r, I solve for v:

2m/7.3 sec = 0.274 m/s

then ω = (0.274 m/s)/(0.014 m) = 19.6.

what am I doing wrong? the correct answer is 39.1
 
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