# Homework Help: Easy Question about power!

1. May 16, 2010

### bon

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. The attempt at a solution

Ok so im 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!

2. May 16, 2010

### bon

Sorry - see it now..ts just P/w right?

3. May 16, 2010

i.e F = P/w