A rim unwinding from a string due to gravity.

The conversation is about a string wrapped around a hoop, with given radius and mass, released from rest and finding its angular speed and speed at its center. In summary, the energy is conserved in this system and the equation used is mgh = (1/2)mv^2 + (1/2)Iw^2, where m is the mass, g is the gravitational acceleration, h is the distance the hoop descended, v is the speed at the center, I is the moment of inertia, and w is the angular speed. However, using this equation may not give the correct answer.
  • #1
Eats Dirt
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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.
 
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  • #2
If I is the moment of inertia of hoop about its centre then,
intial energy = final energy
GPE = KE of translation + KE of rotation
 
  • #3
mgh = (1/2)mv[itex]^{2}[/itex] + (1/2)I[itex]\omega[/itex][itex]^{2}[/itex]
 

FAQ: A rim unwinding from a string due to gravity.

1. What is the phenomenon of a rim unwinding from a string due to gravity?

The phenomenon of a rim unwinding from a string due to gravity refers to the motion of a spinning wheel or rim that is attached to a string or rope and suspended from a fixed point. As the wheel spins, the string gradually unwinds and the wheel moves in a circular motion due to the force of gravity.

2. What causes the rim to unwind from the string?

The rim unwinds from the string due to the force of gravity acting on the wheel. As the wheel spins, the weight of the rim pulls on the string, causing it to unwind and allowing the wheel to move in a circular motion. This is known as centripetal force.

3. Why does the rim move in a circular motion?

The rim moves in a circular motion due to the combination of two forces: the force of gravity pulling the rim down towards the ground, and the tension in the string pulling the rim towards the fixed point. These two forces work together to create a circular motion known as uniform circular motion.

4. How does the speed of the rim affect the unwinding motion?

The speed of the rim affects the unwinding motion in that a faster spinning wheel will have a greater centripetal force, pulling harder on the string and causing it to unwind more quickly. On the other hand, a slower spinning wheel will have a weaker centripetal force and the string will unwind more slowly.

5. Is the phenomenon of a rim unwinding from a string due to gravity affected by other factors?

Yes, the phenomenon of a rim unwinding from a string due to gravity can be affected by other factors such as the length and thickness of the string, the weight and size of the rim, and the distance between the fixed point and the rim. These factors can affect the amount of tension and centripetal force in the system, thus impacting the speed and motion of the rim.

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