Inertia and Torque given Angular Velocity

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SUMMARY

The discussion focuses on calculating the moment of inertia (I0) and friction torque (τf) for a rotor with a moment of inertia IR and outer radius R, influenced by angular velocities α1 and α2. The user correctly identifies that the moment of inertia can be expressed as I = mR², but questions the validity of this simplification. The torque equation τ = Iα is also discussed, with the user uncertain about its application in this context. The conversation emphasizes the need for clarity in applying these fundamental physics equations to the problem at hand.

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  • Understanding of rotational dynamics and moment of inertia
  • Familiarity with torque equations in physics
  • Knowledge of angular acceleration and its implications
  • Basic principles of friction in mechanical systems
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Homework Statement



A rotor of moment of inertia IR and outer radius R spins about a vertical axis. The rotor mount is not friction free. Rather, there is a small constant friction torque of magnitude τf . A string of negligible mass is wound around the outside of the rotor. The string is attached to the rotor in a way that allows it to come free when the end is reached. The other end of the string is attached to a weight of mass m hanging from a massless frictionless pulley. When the system is released from rest the angular velocity of the rotor increases linearly at a rate α1 under the influence of the tension in the string and the torque due to friction. After the string detaches from the rotor, the rotor’s angular acceleration becomes α2 (a negative quantity) due to the friction torque.

Find expressions for I0 and τf in terms of some or all of the quantities α1, α2, m, R, and g the acceleration of gravity.

Homework Equations


I=mR^2
τ=Iα

The Attempt at a Solution


For inertia, would it simply be mR^2? I remember something about a parallel line to the axis of rotation, involving a cross product and all of that... mR^2 seems too easy to be correct...
but if inertia = mR^2, would τ simply be mR^2(α1-α2)?
The τ equation doesn't sound right at all, and I'm somewhat confused on what to do here.

Thanks!
 
Physics news on Phys.org
what is I0 ?
 
OP, do you go to MIT by chance?
 

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