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gills
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Homework Statement
Two disks are mounted on a frictionless vertical shaft of neglible radius.
The lower disk, of mass 440g and radius 3.5cm, is rotating at 180rpm on the frictionless shaft of neglible radius. The upper disk, of mass 270g and radius 2.3cm, is initially not rotating. It drops freely down the shaft onto the lower disk, and frictional forces act to bring the two disks to a common rotational speed.
(a) What is that speed?
(b) What fraction of the initial kinetic energy is lost to friction?
Homework Equations
T = tau
w= omega
R = Radius
m1 = mass lower disk
m2 = mass upper disk
I = rotational inertia = (1/2)mR^2 (for disks)
upper disk = ud
lower disk = ld
alpha = angular acceleration
a(tan) = tangential linear acceleration
t=time
Ok, i will just pop out some equations:
T = I*alpha
w = w0 + alpha*t
a(tan) = alpha*R
K(rotational) = (1/2)Iw^2
The Attempt at a Solution
can we somehow use the K(rotational) equation to solve both?
well first i converted (inital omega of the lower disk) w0(ld) 180rpm = 18.8 rad/s
w0(ud) = 0
we know that wf(ud) = wf(ld) and we need to figure that out
the m has to be in kg so -->
m(ld) = 0.440kg m(ud) = 0.270kg
Kf - Ki = deltaK lost from frictional force?
(1/2)(m1 + m2)*wf^2 - (1/2)(m1)w0^2 = delta K lost?
Any help would be great.