How Long to Increase Spool's Angular Velocity from 11.0 to 35.0 rad/s?

AI Thread Summary
To determine the time required to increase a spool's angular velocity from 11.0 rad/s to 35.0 rad/s under a force of 14.9 N, the angular acceleration must first be calculated using Newton's second law for rotation. The moment of inertia (Icm) is given as 0.490 kg*m^2, and the relationship between torque and angular acceleration can be applied. The torque generated by the force acting at the outer radius of the spool must be considered to find the angular acceleration. Once the angular acceleration is known, the time can be calculated using the change in angular velocity. The discussion emphasizes the need to connect force, torque, and angular motion principles to solve the problem effectively.
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Homework Statement


A spool of thin wire rotates without friction about its axis. A man pulls down on the wire with force of 14.9N. How long does it take to increase the angular velocity of the spool from 11.0rad/s to 35.0rad/s?
Icm = 0.490kg*m^2
Inner radius, r = 0.280m
Outer radius, R = 0.600m

Homework Equations


w=d(theta)/dt
w=v/r


The Attempt at a Solution



im not sure how to do this. i know the equation for angular velocity but i don't know what to do with the force and time
 
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Figure out the angular acceleration using Newton's 2nd law for rotation.
 

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