Zorch, an archenemy of Superman, decides to slow the Earth's rotation to once per 30.5 h by exerting an opposing force at the equator and parallel to it. Superman is not immediately concerned, because he knows Zorch can only exert a force of 4.60 x 107 (comparable to a Saturn V rocket's thrust). Assume the Earth's initial rotation is exactly once per 24.0 h to find how long Zorch must push with this force to accomplish his goal. (This gives Superman time to devote to other villains. The Earth's mass is 5.98 x 1024 kg and its radius is 6.38 × 106 m.) Additional Materials |Reading
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
![**Educational Transcript:**
Zorch, an archenemy of Superman, decides to slow the Earth's rotation to once per 30.5 hours by exerting an opposing force at the equator and parallel to it. Superman is not immediately concerned, as he knows Zorch can only exert a force of \(4.60 \times 10^7 \, \text{N}\) (comparable to a Saturn V rocket's thrust). Assume the Earth's initial rotation is exactly once per 24.0 hours, to determine how long Zorch must push with this force to accomplish his goal. (This gives Superman time to devote to other villains. The Earth's mass is \(5.98 \times 10^{24} \, \text{kg}\) and its radius is \(6.38 \times 10^6 \, \text{m}\.)
[Space to input answer in seconds]
**Additional Materials:**
- [Reading](#)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F310fef68-80b0-4698-99e4-84601aa7983e%2Ffee40c4d-f8fa-42ee-b12b-ac887ece4d42%2F20km0es_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
