Question

Using the law of conservation of angular momentum, estimate how fast a collapsed stellar core would spin if its initial spin rate was 1 revolution per day and its radius decreased from 10,000 km to 10 km.

Answer 1

`\omega_(f) = 1000000\,(rev)/(day)`

Step-by-step explanation:

The law of conservation of angular momentum states that angular momentum remains constant when there is no external moment or forces applied to the system. Let assume that star can be modelled as an sphere, then:

`(2)/(5)\cdot M\cdot R_(o)^(2) \cdot \omega_(o) = (2)/(5)\cdot M\cdot R_(f)^(2) \cdot \omega_(f)`

The final angular speed is:

`\omega_(f) = \omega_(o)\cdot ((R_(o))/(R_(f)))^(2)`

`\omega_(f) = (1\,(rev)/(day) )\cdot ((10000\,km)/(10\,km) )^(2)`

`\omega_(f) = 1000000\,(rev)/(day)`