Qn on Rotational Kinetic Energy

In summary, the Crab Nebula releases energy at a rate of 5x1031 W, obtained from the rotational kinetic energy K of a neutron star at its center. The period of rotation of the neutron star is 0.0331s and it increases by 4.22 x 10-13s per second. The moment of inertia of the neutron star can be calculated by equating the power of the star to a differential equation, with a resulting answer of 1.1x1038."
  • #1
lavieenrose
1
0

Homework Statement


Crab Nebula releases energy at a rate of 5x1031 W, obtaining its energy from the rotational kinetic energy K of a neutron star at its centre.
Period of neutron star's rotation = 0.0331s. T increases by 4.22 x 10-13s per second.

What is the moment of inertia of the neutron star?

Homework Equations


dK/dt = -(4[tex]\pi[/tex]2I/T3) (dT/dt)
This was the first part of the question which I managed to prove already.
*Note: the pi is not supposed to be in superscript.

The Attempt at a Solution


I equated the power of the star to the above differential equation. Solving for I should be quite easy, but somehow my answer (1.1x 1038) is different from the answer provided (1.1 x 1030).
 
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  • #2
Your result looks correct.

ehild
 

What is rotational kinetic energy?

Rotational kinetic energy is the energy an object possesses due to its rotation around an axis. It is dependent on the mass of the object, its moment of inertia, and its angular velocity.

How is rotational kinetic energy calculated?

The formula for calculating rotational kinetic energy is 1/2 * I * ω^2, where I is the moment of inertia and ω is the angular velocity.

What is the difference between rotational kinetic energy and linear kinetic energy?

Rotational kinetic energy is the energy of an object due to its rotation, while linear kinetic energy is the energy of an object due to its motion in a straight line. Rotational kinetic energy is dependent on the object's moment of inertia, while linear kinetic energy is dependent on its mass.

How does rotational kinetic energy relate to real-life applications?

Rotational kinetic energy plays a crucial role in many real-life applications, such as the motion of wheels on a car, the rotation of blades in a wind turbine, and the spin of a ball in sports. Understanding rotational kinetic energy is essential in designing and optimizing these systems.

Can rotational kinetic energy be converted into other forms of energy?

Yes, rotational kinetic energy can be converted into other forms of energy, such as heat, sound, or electrical energy. For example, when a spinning top falls and hits the ground, its rotational kinetic energy is converted into sound and heat energy upon impact.

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