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Homework Statement
A rotating disc is driven by a motor that generates constant power P , and expe-
riences a frictional drag torque
γ ω, where ω is the angular velocity of the disc and γ
is a constant.
If the moment of inertia of the disc is I , show that the time to accelerate
the disc from rest to angular velocity ω is
t= -I/2γ ln (1-w^2/wo^2)
where ω0 is the value of ω in the steady state.
Homework Equations
The Attempt at a Solution
Ok so I am trying to solve this by writing out a differential equation..Torque = rate of change of angular momentum..
Now I know J = Iw so i can write an expression for rate of change of angular momentum..Just having trouble working out what the net torque is..
it is of the form F - γω..but how can i write an expression for F given the power is constant P?
I know the integral of Power dt = the integral of F dw..
Thanks!