Under some circumstances, a star can collapse into an extremely dense object made mostly of neutrons and called a neutron star. the density of a neutron star is roughly 1014 times as great as that of ordinary solid matter. suppose we represent the star as a uniform, solid, rigid sphere, both before and after the collapse. the star's initial radius was 7.0x10^5 km (comparable to our sun); its final radius is 16 km .if the original star rotated once in 35 days, find the angular speed of the neutron star.

The angular speed of the neutron star is

Solution:

As per the question:

Initial radius of the star, r =

Final Radius, r' = 16 km

Period of rotation of the star, T = 35 days =

Now,

To calculate the angular speed of the neutron star:

We use the principle of conservation of angular momentum:

where

I = Moment of inertia

the motion of a pendulum is a classic example of mechanical energy conservation. a pendulum consists of a mass (known as a bob ) attached by a string to a pivot point. as the pendulum moves it sweeps out a circular arc, moving back and forth in a periodic fashion.

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day