Concept explainers
For the satellite system of Prob. 14.9. assuming that the velocity of the base satellite is zero, determine (a) the position
(a)
The position vector r of the mass centre G of the system assuming the base satellite velocity is zero
Explanation of Solution
Given information:
Reference equation from Problem 14.27
Position vectors is written as below
System mass centre is calculated as below,
Substituting the values we get,
Therefore, mass centre position vector is
Conclusion:
Position vector of mass centre is
(b)
The linear momentum L of the system assuming the base satellite velocity is zero
Explanation of Solution
Given information:
Reference equation from Problem 14.27
Position vectors is written as below
Linear momentum is calculated by using the relation,
Substituting the values we get,
Therefore, linear momentum of the system is
Conclusion:
Linear momentum of the system is
(c)
The angular momentum of the system about G assuming the base satellite velocity is zero
Explanation of Solution
Given information:
Reference equation from Problem 14.27
Position vectors is written as below
Angular momentum is calculated by using the relation,
Substituting the values we get,
Therefore, angular momentum of the system is
Assume, mass centre G velocity,
Linear momentum equation can be written as,
Substituting the values we get,
Therefore, individual vector components are,
Angular momentum of the system about origin is
Check whether the above relation satisfies with equation in 14.27
From the above, we can conclude, equation A satisfies with equation B
Conclusion:
Angular momentum of the system is
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Chapter 14 Solutions
Vector Mechanics For Engineers