document.write( "Question 1182825: A small particle is placed at the edge of a phonograph turntable of diameter 30 cm. If the turntable rotates at 45 revolutions per minute, what must be the coefficient of friction so the particle will bot slide out? \n" ); document.write( "

Algebra.Com's Answer #812921 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "A small particle is placed at the edge of a phonograph turntable of diameter 30 cm. If the turntable rotates
\n" ); document.write( "at 45 revolutions per minute, what must be the coefficient of friction so the particle will $\"highlight%28cross%28bot%29%29\"$ not slide out?
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document.write( "It is easy.\r\n" );
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document.write( "Simply EQUATE the centripetal force and the friction force.\r\n" );
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document.write( "The centripetal force acting to the particle is\r\n" );
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document.write( "     = .        (1)\r\n" );
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document.write( "The friction force is   = k*m*g,  where m is the mass of the particle, k is the friction coefficient and g is the gravity acceleration.\r\n" );
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document.write( "So, the equation takes the form\r\n" );
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document.write( "     = k*m*g.     (2)\r\n" );
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document.write( "Cancel the mass \"m\" in both sides\r\n" );
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document.write( "     = k*g.           (3) \r\n" );
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document.write( "Use  v =  =  =  = 0.7065  m/s  (the linear speed).\r\n" );
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document.write( "So, your equation (3) takes the form\r\n" );
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document.write( "     = 10k,   or   10k = 3.328\r\n" );
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document.write( "which gives for the friction coefficient k\r\n" );
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document.write( "    k =  = 0.3328   (dimensionless value).\r\n" );
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document.write( "ANSWER.  The friction coefficient should be at least 0.3328.\r\n" );
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