A high-speed flywheel in a motor is spinning at $500\,\text{rpm}$ when a power failure suddenly occurs. The flywheel has a mass of $40\,\text{kg}$ and a diameter of $75\,\text{cm}$. The power is off for $30\,\text{s}$ and during this time the flywheel slows due to friction in its axle bearings. During this time the flywheel makes $200$ complete revolutions.

Question

A high-speed flywheel in a motor is spinning at $500\,\text{rpm}$ when a power failure suddenly occurs. The flywheel has a mass of $40\,\text{kg}$ and a diameter of $75\,\text{cm}$. The power is off for $30\,\text{s}$ and during this time the flywheel slows due to friction in its axle bearings. During this time the flywheel makes $200$ complete revolutions.(a) At what rate is the flywheel spinning when the power comes back on?
, (b) If the power had not come back, how long would it have taken for the flywheel to stop and how many revolutions would it have made during this time?
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Jason · Accepted Answer

Part (a): $\boxed{10\pi\,\text{rad/s}}$ (which is equivalent to 300 rpm).\nPart (b): $\boxed{75\,\text{s}}$ to come to a complete stop with a total of $\boxed{312.5\,\text{rev}}$.

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