A rim unwinding from a string due to gravity.

[Eats Dirt]

Homework Statement

A string is wrapped around a small hoop several times. the radius is 8cm and mass 0.18 kg. the string is released from rest after the hoop has descended 75 cm what is the angular speed of the rotating hoop and the speed at its centre?

Homework Equations

mgh 1/2 Iw^2

The Attempt at a Solution

MGH energy is conserved so mgh=1/2Iw^2
i sub in and solve except this doesn't give the right answer.

 

[grzz]

If I is the moment of inertia of hoop about its centre then,
intial energy = final energy
GPE = KE of translation + KE of rotation

 

[grzz]

mgh = (1/2)mv$^{2}$ + (1/2)I$\omega$$^{2}$