Concept explainers
If there were a great migration of people toward the Earth’s equator, would the length of the day (a) get longer because of conservation of
The change that happens to the length of the day if there were a great migration of people toward the Earth’s equator.
Answer to Problem 1Q
Option (a)
Explanation of Solution
Moment of inertia is the sum of the products of the mass of each particle in a body with the square of its distance from the axis of rotation. The migration of more people towards the earth’s equator may result in the accumulation of more mass from the axis of rotation. As a result the moment of inertia of the Earth would increase.
The relation between the angular momentum and the moment of inertia is given by,
Here,
According to the conservation of angular momentum, the increase in moment of inertia will automatically decrease the Earths angular velocity. Thus the length of the day would increase.
Conclusion:
Since the angular momentum and the angular velocity are related option (a) is the correct answer.
Length of the day is increasing as a result of angular momentum so option (b) is the incorrect answer.
Since the length of the day is increasing option (c) is the correct answer.
Since the length of the day does not depends on the conservation of energy option (d) is incorrect.
The length of the day is increasing due to the angular momentum option (e) is incorrect.
Want to see more full solutions like this?
Chapter 11 Solutions
Physics for Scientists and Engineers (Chaps 1-38)
Additional Science Textbook Solutions
Physics: Principles with Applications
Physics (5th Edition)
College Physics: A Strategic Approach (4th Edition)
College Physics: A Strategic Approach (3rd Edition)
Cosmic Perspective Fundamentals
Lecture- Tutorials for Introductory Astronomy
- If you know the velocity of a particle, can you say anything about the particle’s angular momentum?arrow_forwardFigure 13.24 shows a particle with momentum p. Using the coordinate systems shown, determine the direction of the angular momentum of the particle around the origin in each case, and write expressions for L, using symbols defined in Figure 13.23. FIGURE 13.24arrow_forwardIf the torque acting on a particle about an axis through a certain origin is zero, what can you say about its angular momentum about that axis?arrow_forward
- Big Ben (Fig. P10.17), the Parliament tower clock in London, has hour and minute hands with lengths of 2.70 m and 4.50 m and masses of 60.0 kg and 100 kg, respectively. Calculate the total angular momentum of these hands about the center point. (You may model the hands as long, thin rods rotating about one end. Assume the hour and minute hands are rotating at a constant rate of one revolution per 12 hours and 60 minutes, respectively.)arrow_forwardFor a particle traveling in a straight line, are there any points about which the angular momentum is zero? Assume the line intersects the origin.arrow_forwardIf a particle is moving with respect to a chosen origin it has linear momentum. What conditions must exist for this particle’s angular momentum to be zero about the chosen origin?arrow_forward
- A thin rod of length 2.65 m and mass 13.7 kg is rotated at anangular speed of 3.89 rad/s around an axis perpendicular to therod and through one of its ends. Find the magnitude of the rodsangular momentum.arrow_forwardTwo astronauts (Fig. P10.67), each having a mass of 75.0 kg, are connected by a 10.0-m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 5.00 m/s. Treating the astronauts as particles, calculate (a) the magnitude of the angular momentum of the two-astronaut system and (b) the rotational energy of the system. By pulling on the rope, one astronaut shortens the distance between them to 5.00 m. (c) What is the new angular momentum of the system? (d) What are the astronauts new speeds? (e) What is the new rotational energy of the system? (f) How much chemical potential energy in the body of the astronaut was converted to mechanical energy in the system when he shortened the rope? Figure P10.67 Problems 67 and 68.arrow_forwardA solid cylinder of mass 2.0 kg and radius 20 cm is rotating counterclockwise around a vertical axis through its center at 600 rev/min. A second solid cylinder of the same mass and radius is rotating clockwise around the same vertical axis at 900 rev/min. If the cylinders couple so that they rotate about the same vertical axis, what is the angular velocity of the combination?arrow_forward
- Check Your Understanding Which has greater angular momentum: a solid sphere of mass m rotating at a constant angular frequency 0 about the z-axis, or a solid cylinder of same mass and rotation rate about the z-axis?arrow_forwardTwo astronauts (Fig. P10.67), each having a mass M, are connected by a rope of length d having negligible mass. They are isolated in space, orbiting their center of mass at speeds v. Treating the astronauts as particles, calculate (a) the magnitude of the angular momentum of the two-astronaut system and (b) the rotational energy of the system. By pulling on the rope, one of the astronauts shortens the distance between them to d/2. (c) What is the new angular momentum of the system? (d) What are the astronauts new speeds? (e) What is the new rotational energy of the system? (f) How much chemical potential energy in the body of the astronaut was converted to mechanical energy in the system when he shortened the rope? Figure P10.67 Problems 67 and 68.arrow_forwardRepeat Example 10.15 in which the stick is free to have translational motion as well as rotational motion.arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University
- Glencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-HillPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning