A system of three particles with masses m₁ = 8m at position (0, 0, -d), m2 = 7m at position (d, 0, d),and m3 = 5m at position (0, d, 0) has an inertia tensor of I = md²What are the principal moments of inertia of the system?20 0 71022 07 012about the origin.Enter the moments of inertia from smallest to largest.First moment = Ex: 1.23md²Second moment = Ex: 1.23md²Third moment = Ex: 1.23md²

The inertia tensor of the system is I=md2⎝⎛200702207012⎠⎞;We can find principal moments and…

Answered: A system of three particles with masses…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A system of three particles with masses m₁ = 5m at position (0, 0, -d), m2 = 7m at position (d, 0, d), 15 0 7 and m3 = 3m at position (0, d, 0) has an inertia tensor of I = md² 0 19 0 about the origin. 7 0 10 What are the principal moments of inertia of the system? Enter the moments of inertia from smallest to largest. First moment = Ex: 1.23 Second moment = Ex: 1.23 Imd² Third moment = Ex: 1.23 md² md²
(4) A particle moves from point (1,2,3) to point (3,5,2) under the action of force F₁ = 2 i + j + 3k and F₂ = 31-4j-2k. Find the work done by the force.
Use Green's theorem to calculate the work done by the force F(x, y) = xy'i + 3x?yj on a particle that is moving counterclockwise around the triangle with vertices (-3, 0), (0, 0), and (0, 3).
Find the position r(t) acceleration a(t) = (3 cos t, 2 sin t, 2)- v(0) = (0,0, 1) of a particle that begins at r(0) = (2, 1,0) and has and initial velocity Select one: a. r(t) = (5+ 4t - 3 cos t, 1-t-2 sin t, t2 + 2t) b. r(t) = (5 – 3 cos t, 1 + 2t- 2 sin t, t2 + t) C. r(t) = (5 +2t – 3 cos t, 1 +3t - 2 sin t, t² +t+ 1) d. r(t) = (4+t-3 cos t, 2+ 3t – 2 sin t, t2) e. r(t) = (5 -t- 3 cos t, 1 +t-2 sin t, t2)
A projectile is fired northward from a height of 420 m. Assuming that the x-axis is pointing east, O representing ground level. The projectile's y-axis is pointing north and the z-axis is pointing up with z = initial velocity vector is v(0) = (0, 99, 22). In addition to a downward gravitational acceleration of 9.8 m/s², it experiences in flight an westward acceleration of 5 m/s² due to the wind. Find the projectile's velocity and position vectors t seconds after the projectile is fired.
take C=1
A particle travels along the helix C given by (t) = cos ti + sin tj + 2tk and is subject to a force F = xi + zj - xyk. Find the total work done on the particle by the force for 0
B/ show that if u(t) = à cos t + b sin t, where a and b* are constant vectors |du d'u dt then ü(t). = 0 كلية العلوم بالفرعية

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