Angular speed of wrapper string

AI Thread Summary
To solve the problem of the angular speed of a hoop with a string wrapped around it, energy conservation principles should be applied. The kinetic energy (KE) of the hoop and the gravitational potential energy (PE) must be considered, where KE is calculated as (1/2)*m*v^2 and PE as mgh. The relationship between linear speed and angular speed can be established through the hoop's radius. After the hoop descends 60.0 cm, the angular speed can be determined using these equations. This approach will yield the required angular speed and the speed at the center of the hoop.
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Homework Statement




A string is wrapped several times around the rim of a small hoop with radius 8.00 cm and mass 0.180 kg . The free end of the string is held in place and the hoop is released from rest (the figure ). After the hoop has descended 60.0 cm, calculate angular speed and speed at the center

Homework Equations


w= omega

w = w+ at
K = 1/2 I w^2 ?



The Attempt at a Solution



I'm really unsure how to approach this problem and don't exactly know where to start
 
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Use energy conservation. Add linear KE=(1/2)*m*v^2 and gravitational potential energy PE=mgh to your list of equations.
 

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