Inertia and Torque given Angular Velocity

AI Thread Summary
The discussion centers on a physics problem involving a rotor with a moment of inertia and friction torque, where a string attached to a weight influences the rotor's angular velocity. Participants are trying to derive expressions for the moment of inertia (I0) and the friction torque (τf) based on given variables like angular accelerations (α1, α2), mass (m), radius (R), and gravitational acceleration (g). There is confusion regarding the correct formulation of inertia, with one participant questioning if it can simply be mR^2 and expressing uncertainty about the torque equation. The conversation highlights the need to consider the effects of friction and the transition from the rotor's initial acceleration to its behavior after the string detaches. The thread reflects a collaborative effort to clarify the physics concepts involved in the problem.
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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?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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