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In grinding certain tools the linear velocity of the the grinding surface should not exceed 6000 ft/s. Find the maximum number of revolution of a 12 inch diameter wheel?

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    What have you tried? Do you understand the relationship between angular velocity and linear velocity?2012-06-25

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This involves precisely the same notions as your other recent questions. The circumference of the grinding wheel (in feet) is $\pi$. So if the thing is going at $r$ revolutions per second, the linear speed of the outer part of the grinding surface is $\pi r$ feet per second. This speed should be $\le 6000$ feet per second. So the largest allowed $r$ is the one for which $\pi r=6000$. Now solve for $r$.

By the way, $6000$ feet per second seems awfully fast!

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    That's a little under three times the muzzle velocity of an AK-47, and about $16\%$ of the Earth's escape velocity ...2012-06-25