Example 9-2 - 9-11 ), where r i is the radial distance from...

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A Rotating System of Particles An object consists of four point particles, each of mass  m , connected by rigid massless rods to  form a rectangle of edge lengths 2 a  and 2 b,  as shown in  Figure       9-3     . The system rotates with  angular speed   about an axis in the plane of the figure through the center, as shown. ( ω a ) Find  the kinetic energy of this object using  Equation       9-11      and  Equation       9-12     . ( b ) Check your result by  individually calculating the kinetic energy of each particle and then taking their sum. PICTURE  Because we are given that the objects are point particles, we use  Equation       9-11      to  calculate  I  and then use  Equation       9-12      to calculate  K . SOLVE ( a ) 1. Apply the definition of moment of inertia  ( Equation  
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Unformatted text preview: 9-11 ), where r i is the radial distance from the rotation axis to the particle of mass m i : Answer: 2. The masses m i and the distances r i are given: Answer: 3. Substitution gives the moment of inertia: Answer: 4. Using Equation 9-12 , solve for the kinetic energy: Answer: ( b ) 1. To find the kinetic energy of the i th particle, we must first find its speed: Answer: 2. The particles are all moving in circles of radius a . Find the speed of each particle: Answer: 3. Substitute into the Part-( b ) step-1 result: Answer: 4. Each particle has the same kinetic energy. Sum the kinetic energies to get the total: Answer: 5. Compare with the Part-( a ) result: Answer:...
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This note was uploaded on 11/29/2010 for the course PHYS 1301W taught by Professor Marshak during the Spring '08 term at Minnesota.

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Example 9-2 - 9-11 ), where r i is the radial distance from...

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