How Does Angular Acceleration Affect Angular Velocity?

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SUMMARY

The discussion focuses on calculating the angular velocity of a solid cylinder grinding wheel after a constant tangential force is applied. Given a radius of 0.330 m, an angular acceleration of 0.984 rad/s², and a time interval of 4.30 seconds, the angular velocity can be determined using the formula ω = αt. The moment of inertia is provided as 90.457 kg/m², and the mass of the wheel is 1661.29 kg. The solution confirms that the angular velocity after the specified time is 4.23 rad/s.

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  • Understanding of angular motion concepts
  • Familiarity with the moment of inertia
  • Knowledge of angular acceleration and its relationship to angular velocity
  • Ability to apply basic physics equations related to rotational dynamics
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  • Study the derivation of the angular velocity formula ω = αt
  • Explore the relationship between torque, moment of inertia, and angular acceleration
  • Learn about the effects of friction on rotational motion
  • Investigate real-world applications of angular motion in engineering
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Homework Statement


A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 270 N applied to its edge causes the wheel to have an angular acceleration of 0.984 rad/s2.

If the wheel starts from rest, what is its angular velocity after 4.30 s have elapsed, assuming the force is acting during that time?

Homework Equations


Moment of intertia is 90.457kg/m2
mass of wheel is 1661.29kg


The Attempt at a Solution



I was able to find moment of inertia and mass of wheel above...not sure about angular velocity. I can't find the right equation what uses I.
 
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nm...it was just w=at
 

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