Explanation Given information: The weight of the space probe ( W ) is 3000 lb , the radius of gyration along x axis is 1.375 ft , the radius of gyration along y axis is 1.425 ft , the radius of gyration along z axis is 1.250 ft , the mass of meteorite ( m ) is 5 oz and the relative velocity of the meteorite ( v 0 ) is ( 2400 ft / s ) i + ( 3000 ft / s ) j + ( 3200 ft / s ) k and the position vector is ( 9 ft ) i + ( 0.75 ft ) k . Write the expression for the angular momentum of the meteorite about G . ( H G ) M = r A + m M v 0 ...... (I) Here, the position vector is r A . Write the expression for the angular momentum of the probe. ( H G ) P = I x ω x i + I y ω y j + I z ω z k ...... (II) Here, the angular velocity along the x axis is ω x , the angular velocity along the y axis is ω y , the angular velocity along the z axis is ω z , the moment of inertia about the x axis is I x , the moment of inertia about the y axis is I y and the moment of inertia about the z axis is I z . Write the expression for the moment of inertia along x axis. I x = m k x 2 ...... (III) Here, the mass of the probe is m and the radius of gyration along x axis is k x . Write the expression for the moment of inertia along y axis. I y = m k y 2 ...... (IV) Here, the radius of gyration along y axis is k y . Write the expression for the moment of inertia along z axis. I z = m k z 2 ...... (V) Here, the radius of gyration along z axis is k z . Substitute m k x 2 for I x , m k y 2 for I y and m k z 2 for I z in Equation (II). ( H G ) P = m k x 2 ω x i + m k y 2 ω y j + m k x 2 ω z k = m ( k x 2 ω x i + k y 2 ω y j + k x 2 ω z k ) ...... (VI) Write the expression relation between the angular momentum of the meteorite and the angular momentum of the probe. ( H G ) P = 0.20 ( H G ) W ...... (VII) Write the expression for the angular momentum of three-dimensional plane. ω = ω x i + ω y j + ω z k ...... (VIII) Calculation: Substitute ( 9 ft ) i + ( 0.75 ft ) k for r A , ( 2400 ft / s ) i + ( 3000 ft / s ) j + ( 3200 ft / s ) k for v 0 , 5 oz for m M in Equation (I). ( H G ) M = [ [ ( 9 ft ) i + ( 0.75 ft ) k ] × 5 oz 32.2 ft / s 2 [ ( 2400 ft / s ) i + ( 3000 ft / s ) j + ( 3200 ft / s ) k ] ] = [ [ ( 9 ft ) i + ( 0.75 ft ) k ] × 5 oz 32.2 ft / s 2 1 lb 16 oz [ ( 2400 ft / s ) i + ( 3000 ft / s ) j + ( 3200 ft / s ) k ] ] = [ [ 9.705 × 10 − 3 lb ⋅ s 2 / ft ] ( − 27 k − 28

12th Edition

ISBN: 9781259977305

Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.

Publisher: Mcgraw-hill Education,

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Chapter 18.1, Problem 18.33P

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The angular velocity of the probe.

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The angular velocity of the probe.

Solution Summary: The author explains the angular velocity of the space probe and the position vector for the meteorite.

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The angular velocity of the probe.

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