Neutron stars are known to be incredibly dense. According to our text, if a mere teaspoon of them were placed on earth, it would weigh approximately one-hundred-million tons! (pg 357)

The high-speed rotation of a neutron star is explained by conservation of angular momentum. Linear momentum can be defined as an object of mass (m) moves with speed (v) in a straight line. However, when an object moves with an angular speed (ω) along the circumference of a circle of radius (r), it is defined as angular momentum. The formula for angular momentum is as follows:

L = Iω

Where:

L = Angular momentum

I = Moment of inertia

ω = Angular velocity

Angular momentum is proportional to the moment of inertia and its angular velocity. Angular momentum is proportional to the moment of inertia and its angular velocity. The moment of inertia is dependent on the distribution of mass inside the body. The further and widely distributed its mass is, the more its moment of inertia will be. For example, if you were to sit on a spinning chair and spin on it with arms outstretched you would have a wider mass distribution from the axis. However, you could experience a smaller moment of inertia if you were to hold your arms closer to your chest because you would be distributing your mass closer to the axis.

Likewise, the high speed a neutron star experiences has a similar effect in its rotation. In the absence of the external torque, angular momentum is conserved. As the star collapses into a neutron star, its radius decreases and as does its inertia. To maintain angular momentum, the angular velocity increases, resulting in such a high speed of rotation. This is why a neutron star rotates at a higher speed than most stars, such as our sun.

When an object is lifted up it gains in potential energy. Where is the potential energy stored?

When someone lifts an object, that person exerts energy which will become kinetic energy when the object is dropped. This is known as gravitational potential energy, the energy an object possesses due to its position in a gravitational field. This energy is stored in the object being lifted as the result of its vertical position or height. Gravitational potential energy is stored as a result of gravitational attraction between the earth and the object. Gravitational potential energy depends on the mass of the object and the height to which it is raised. The more mass an object possesses, the greater the gravitational potential energy. Likewise, the higher an object is elevated, the greater the gravitational potential energy. When an object is lifted to a new position, there is an increase in potential energy

The formula for gravitational potential energy is:

Ug = mgh

Where:

Ug = Gravitational Potential energy

m = Mass

g = Acceleration due to Gravity

h = height

Gravitational potential energy is based on the potential energy gravity will have on an object. Potential energy is due to the configuration of a system. In this case, the energy is stored in the system formed by the object, earth, and the gravitational field. Therefore, gravitational potential energy is energy stored in the gravitational field. The energy will be released as kinetic energy when the object is dropped, thus allowing gravity to pull the object to the earth.

Here is my response to my teachers question about question 2:

Dr. Ricardo,

Rotational inertia is the property of a mass to resist rotational motion. The inertia from past weeks was related to translation of motion. That inertia can be defined as the property of a mass to resist translation. Rotational inertia is the property of mass to resist rotation.

Could you please clarify what you mean specifically by "the physics we are studying?" Do you mean this week's topics or a general, broader meaning?

Do these sound like good responses?