H_Chapter 8_answer_homework_students

H_Chapter 8_answer_homework_students - Chapter 8 Rotational...

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Chapter 8 Rotational Kinetic Energy & Rotational Inertia 4. Find the rotational inertia of the system of point particles shown in the figure assuming the s ystem rotates about the (a) x - axis, (b) y - axis, (c) z -axis. The z - axis is perpendicular to the xy - plane and points out of the page. Point particle A has a mass of 200 g and is located at ( x, y, z ) = ( 3.0 cm, 5.0 cm, 0), point particle B has a mass of 300 g and is at (6.0 cm, 0, 0), and point particle C has a mass of 500 g and is at (– 5.0 cm, 4.0 cm, 0). (d) What are the x - and y - coordinates of the center of mass of the system? a) The rotational inertia about the x axis is - The distance R A from A to the x - axis is R A = y A = 5.0cm - The distance R B from B to the x - axis is R B = y B = 0cm - The distance R C from C to the x - axis is R C = y C = - 4.0cm 2 2 2 2 2 . 000 , 13 ) 0 . 4 )( 500 ( ) 0 )( 300 ( ) 0 . 5 )( 200 ( cm g cm g cm g cm g r m I i i C A i x b) The rotational inertia about the y axis is - The distance R A from A to the y - axis is R A = x A = - 3.0cm - The distance R B fro m B to the y axis is R B = x B = 6.0 cm - The distance R C from C to the y axis is R C = x C = - 5.0cm 2 2 2 2 2 (200 g)(3.0 cm) (300 g)(6.0 cm) (500 g)(5.0 cm) 25,000 g cm C y i i i A I m r c) The rotational ine rt ia about the z axis - The distance to R A From to the z axis is R A = z A = v(x 2 A +y 2 A ) - The distance to R B From to the z axis is R B = z B = v( x 2 B + y 2 B ) - The distance to R C From to the z axis is R B = z B = v(x 2 B +y 2 B ) B A x y B A C x y z x y R C
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2 2 2 2 2 2 ) 0 . 4 ( ) 0 . 5 ( ) 500 ( ) 0 . 6 )( 300 ( ) 0 . 5 ( ) 0 . 3 ( ) 200 ( cm cm g cm g cm cm g r m I i i C A i z I z = 38,000g.cm 2 So l ving t his problem will be of great use further ion Phys214 0. This solution overwrite any other . The comb ination of rotation through 3 axis is over the scope of this class d) The x and y coordi nates of the center of mass of the system cm g g g cm g cm g cm g m m m y m y m y m m y m y cm g g g cm g cm g cm g m m m x m x m x m m x m x C B A C C B B A A i i i cm C B A C C B B A A i i i cm 0 . 1 500 300 200 ) 0 . 4 ( 500 ) 0 ( 300 ) 0 . 5 ( 200 3 . 1 500 300 200 ) 0 . 5 ( 500 ) 0 . 6 ( 300 ) 0 . 3 ( 200 - ---------------------------------------------------------
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