Easy angular velocity question

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SUMMARY

The discussion centers on calculating the final angular velocity of a solid disk with a radius of 1.4 cm and 2.0 m of string unwound over 7.3 seconds. The correct final angular velocity is determined to be 39.1 rad/s, while the user incorrectly calculated it as 19.6 rad/s. The user applied the formula ω = v/r, where v is the linear velocity derived from the string unwound, but failed to account for the constant acceleration due to the applied force.

PREREQUISITES
  • Understanding of angular velocity and its relationship to linear velocity
  • Familiarity with the formula v = r * ω
  • Basic knowledge of rotational dynamics and constant acceleration
  • Ability to perform unit conversions (e.g., cm to m)
NEXT STEPS
  • Review the principles of rotational motion and angular acceleration
  • Study the effects of constant force on linear and angular acceleration
  • Learn about the relationship between linear distance and angular displacement
  • Explore examples of calculating angular velocity in different scenarios
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Students studying physics, particularly those focusing on rotational dynamics, as well as educators seeking to clarify concepts related to angular velocity and acceleration.

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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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