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University Physics Volume 3

17th Edition
William Moebs + 1 other
ISBN: 9781938168185
BuyFindarrow_forward

University Physics Volume 3

17th Edition
William Moebs + 1 other
ISBN: 9781938168185
Textbook Problem

The core of a star collapses during a supernova, fanning a neutron star. Angular momentum of the core is conserved, so the neutron star spins rapidly. If the initial core radius is 5.0 × 10 5 km and it collapses to 10.0 km, find the neutron star's angular’ velocity in revolutions per second, given the core’s angular’ velocity was originally 1 revolution per 30.0 days.

To determine

Neutron star's angular velocity.

Explanation

Given:

  ri = 5.0×105km

  rf = 10km

  Ti =30days

Formula used:

Angular velocity is calculated by

  vf=(r2ir2f)vi

Calculation:

The angular momentum of a rotating body is given as follows

  L=Iω

Here I is the moment of inertia and ω is the angular frequency.

In the formation of a neutron star, the angular momentum is conserved.

Hence, Iiωi=Ifωf

Here, Ii and If are the initial and final moment of inertia and are the initial and final angular velocity.

By the relation ω=2πv we get

  Ii(2πvi)=If(2πvf)Iivi=Ifvf

On rearranging, vf=(IiIf)vi

Since I is directly proportional to the square of the radius, the ratio of moment of inertia can be replaced ratio of squares of the radius

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