Angular Acceleration Homework: Find w/ Radius, Mass

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SUMMARY

The discussion focuses on calculating the angular acceleration of a hoop with a radius of 0.08m and a mass of 0.18kg as a string unwinds from it. The correct angular acceleration is determined to be 123 rad/sec². The solution involves using the relationship between torque and angular acceleration, specifically τ = Iα, where torque τ is calculated as the product of force and distance. The moment of inertia is derived from the formula MR², leading to the conclusion that the torque equation must balance with the moment of inertia to find the angular acceleration.

PREREQUISITES
  • Understanding of torque and angular acceleration
  • Familiarity with the moment of inertia formula (I = MR²)
  • Basic knowledge of rotational dynamics
  • Ability to manipulate equations involving angular motion
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  • Study the derivation of the moment of inertia for different shapes
  • Learn about the relationship between linear and angular quantities in physics
  • Explore advanced torque applications in rotational systems
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This discussion is beneficial for physics students, mechanical engineers, and anyone studying rotational dynamics and torque in mechanical systems.

moondawg
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Homework Statement


A string is wrapped several times around the rim of a small hoop with radius .08m and mass .18kg. The free end of the string is pulled upward in just the right way so that the hoop doesn't move vertically as the string unwinds. Find the angular acceleration of the hoop as the string unwinds.


Homework Equations





The Attempt at a Solution


So at first i thought i would use 2 equations of torque to find the ang accel(I\alpha=Fd) but that didnt give me the correct answer in the back of the book of 123 rad/sec2. So my friend helped me out and said to set radius x mass equal to MR2\alpha. and that did give me the correct answer i just don't see the logic in setting those 2 equal to each other bc why would r x m be on one side of the equation?! Pleassseee help!
 
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Find torque

τ = Fd
d is perpendicular distance

and hope you can find moment of inertia of the body

...

then use

τ = Iα
 

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