Chapter 10: Problem 46
Suppose that an asteroid traveling straight toward the center of the earth were to collide with our planet at the equator and bury itself just below the surface. What would have to be the mass of this asteroid, in terms of the earth's mass \(M\), for the day to become 25.0% longer than it presently is as a result of the collision? Assume that the asteroid is very small compared to the earth and that the earth is uniform throughout.
Short Answer
Step by step solution
Understand the Problem
Apply Conservation of Angular Momentum
Set Up Equation for Angular Velocities
Simplify and Solve for the Mass of the Asteroid
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Conservation of Angular Momentum
Moment of Inertia
- An object with a larger moment of inertia requires more energy to change its state of rotation compared to one with a smaller moment of inertia.
- This idea is analogous to trying to spin a computer chair versus a small paper fan; the chair, having more inertia, is harder to rotate quickly.