(A) What is the angular speed of the pulsar?
Angular Speed Calculation:
The angular speed of the pulsar can be calculated using the formula: angular speed = 2π / period.
Given the period of the pulsar as 2.7575 seconds, substituting the values:
angular speed = 2π / 2.7575
angular speed ≈ 2.277 rad/s
(B) What would be the rotational inertia of the neutron star modeled as a uniform sphere?
Rotational Inertia Calculation:
The rotational inertia of a uniform sphere is calculated using the formula:
Rotational Inertia = (2/5) * mass * radius^2.
Substituting the mass of the pulsar and the effective radius provided:
Rotational Inertia ≈ 1.37 x 10^38 kgm^2
(C) What is the rotational (kinetic) energy of the pulsar?
Rotational Energy Calculation:
The rotational energy of the pulsar is determined using the formula:
Rotational Energy = (1/2) * rotational inertia * angular speed^2.
Substituting the values obtained for rotational inertia and angular speed:
Rotational Energy ≈ 3.55 x 10^38 J
(D) How much rotational kinetic energy is lost by the pulsar in one second?
Change in Rotational Energy Calculation:
The change in rotational kinetic energy is calculated by the formula:
Change in Rotational Energy = -angular speed * change in angular speed * rotational inertia.
Substituting the given values for change in angular speed and rotational inertia:
Change in Rotational Energy ≈ -5.286 x 10^26 J