Neutron stars are extremely dense objects that are formed from the remnants of supernova explosions. Many rotate very rapidly. Suppose the mass of a certain spherical neutron star is twice the mass of the Sun and its radius is 10.0 km. Determine the greatest possible angular speed the neutron star can have so that the matter at its surface on the equator is just held in orbit by the gravitational force.
Gravitational force
In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.
Acceleration Due to Gravity
In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.
![**Understanding Neutron Stars and Their Rotation**
**Concept Overview:**
Neutron stars are incredibly dense celestial objects formed from the remnants of supernova explosions. Due to their density, they possess unique properties, including the ability to spin rapidly. This text explores a scenario involving such a star to calculate its angular speed.
**Problem Statement:**
We are given a spherical neutron star with the following characteristics:
- Mass: Twice that of the Sun.
- Radius: 10.0 km.
**Objective:**
Determine the greatest possible angular speed at which the neutron star can rotate without causing the matter at its surface on the equator to break away from its gravitational force.
**Solution Approach:**
- Consider the balance between gravitational and centrifugal forces to ensure stability.
- Use Newton's Law of Gravitation alongside rotational dynamics.
- Equate these forces to solve for the angular speed that ensures matter on the equator remains in orbit without separating from the star’s gravitational influence.
This educational exercise involves applying principles of physics, specifically mechanics and gravitational theory, to understand the behavior of astronomical phenomena under extreme conditions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21ec5513-8136-491c-9bc9-2f1a8372f6ef%2F3ac81394-2af5-46ea-ae5e-dead914a4a0e%2F2pjtpt_processed.png&w=3840&q=75)
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