   Chapter 7, Problem 48AP

Chapter
Section
Textbook Problem

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.

To determine
The greatest possible angular speed of the neutron star so that the matter at its surface on the equator is just held in orbit by the gravitational force.

Explanation

Given Info:

The mass of the neutron star is twice the mass of the sun and the radius of the neutron star is 10.0km .

Explanation:

The centripetal force is provided by the small parts of the material in the star’s equator.

Thus,

GMmR2=m(Rω2)

• ω is the angular speed of the neutron star
• G is gravitational constant
• M is the mass of neutron star
• m is the mass of parts in the equator
• R is the radius of the neutron star

Formula to calculate the angular speed of the neutron star is,

ω=GMR2

Substitute 6.67×1011Nm2kg2 for G, 2(1.99×1030kg) for M and 10.0km for R to find the angular speed of the star,

ω=(6

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