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Work
has to be done on the wheel to decrease its rotational kinetic energy. The decrease
in rotational kinetic energy depends on the torque (FDr) acting on the wheel
and the total number of radians, q, that
the wheel rotates in going between two rotational kinetic energy values.
(FDr)
= I(w12
- w22)/2. This expression
may be used to estimate the bearing torque if this is the dominant energy loss
process.
The same torque may be evaluated by considering the angular
momentum of the wheel system. At an angular velocity, w, the angular momentum is Iw.
If a torque is applied to the system the angular momentum changes because
the angular velocity changes. If the time, t, for the wheel system to go between
two values of the angular velocity is measured then: (FDr) t = I(w1 -w2). From this relation:
(FDr) = I(w1 -w2)/t.
Compute the bearing torque using this expression. Does it agree with the
value obtained from the rotational kinetic energy calculation?
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