Concept explainers
The total
Answer to Problem 55PQ
The total angular momentum of the system is
Explanation of Solution
The rotating system considered here is the Earth – Moon system. The total angular momentum of the system is equal to the sum of angular momentum of Moon orbiting the earth, the Moon’s rotational angular momentum, and the Earth’s rotational angular momentum. All these are acting in the same direction.
Write the equation to find the orbital angular momentum of Moon.
Here,
Write the equation to find the orbital speed of the Moon.
Here,
The orbit of Moon around the earth is circular. Therefore the distance travelled by Moon is equal to the perimeter of the circular orbit which is
Rewrite equation (II).
Substitute equation (III) in (I) to get
Now the equation for Moon’s rotational angular momentum is to be found.
Write the equation to find Moon’s rotational angular momentum.
Here,
Here Moon can be treated as a solid sphere to find the moment of inertia.
Write the equation to find the momentum of inertia of moon.
Here,
Substitute above equation in (V).
Write the equation to find the angular velocity of moon.
Here,
Since the same side of moon always faces the earth, its orbital period is equal to the rotational period of moon. Thus replace
Same procedure used to find the rotational angular momentum of Earth also.
Write the equation to find Earth’s rotational angular momentum.
Here,
Write the equation to find the momentum of inertia of Earth.
Here,
Substitute above equation in (VIII).
Write the equation to find the angular velocity of earth.
Here,
Substitute above equation in equation (IX).
The total angular momentum of the system is equal to the sum of angular momentum of Moon orbiting the earth, the Moon’s rotational angular momentum, and the Earth’s rotational angular momentum.
Write the equation to find the total angular momentum of the system.
Here,
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, the total angular momentum of the system is
Want to see more full solutions like this?
Chapter 13 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
- Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON