What is the Time to Accelerate a Rotating Disc with Frictional Drag Torque?

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SUMMARY

The discussion focuses on calculating the time required to accelerate a rotating disc under the influence of a frictional drag torque. The derived formula for this time is t = -I/2γ ln(1 - ω²/ω₀²), where I is the moment of inertia, γ is the constant frictional drag torque, and ω₀ is the steady-state angular velocity. Participants explored the relationship between torque, angular momentum, and power, ultimately confirming that the force can be expressed as F = P/ω, where P is the constant power generated by the motor.

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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!
 
Physics news on Phys.org
Sorry - see it now..ts just P/w right?
 
i.e F = P/w
 

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