guringpw

2022-01-02

A high-speed flywheel in a motor is spinning at 500 rpm when a power failure suddenly occurs. The flywheel has mass 40.0 kg and diameter 75.0 cm. The power is off for 30.0 s, and during this time the flywheel slows due to friction in its axle bearings. During the time the power is off, the flywheel makes 200 complete revolutions. (a) At what rate is the flywheel spinning when the power comes back on?

Buck Henry

a) The fly wheel spinning when the power comes back
$\theta -{\theta }_{0}=\frac{1}{2}\left({\omega }_{z}-{\omega }_{oc}\right)t$
$2\left(\theta -{\theta }_{0}\right)=\left({\omega }_{z}-{\omega }_{oc}\right)t$
${\omega }_{z}=\frac{2\left(\theta -{\theta }_{0}\right)}{t}-{\omega }_{oc}$
${\omega }_{oc}=500r±$
$=8.33\frac{rev}{s}$
${\omega }_{z}=\frac{2.200rev}{30s}-8.33\frac{rev}{s}$
${\omega }_{z}=\frac{400rev}{30s}-8.33\frac{rev}{s}$
The fly wheel spinning when the power comes back is
${\omega }_{s}=5\frac{rev}{s}$
$=300r±$

Do you have a similar question?