Try the fastest way to create flashcards
Question

# The Sun's mass is$2.0 × 10^{30} kg,$its radius is$7.0 × 10^5 km,$and it has a rotational period of approximately 28 days. If the Sun should collapse into a white dwarf of radius 3.5 × 10³ km, what would its period be if no mass were ejected and a sphere of uniform density can model the Sun both before and after?

Solution

Verified
Step 1
1 of 3

From $\textbf{conservation of angular momentum }$ we know that : $\textbf{ the angular momentum of a system of particles around a point in a fixed inertial reference frame is conserved if there is no net torque around this point }$.

$\sum \tau = \dfrac{d L }{dt} =0$

$\begin{gather*} L_{i} = L_{f} \\ I_{i} \omega_{i} = I_{f} \omega_{f} \\ \end{gather*}$

From $\textbf{the moment of inertia of the sun before it collapses }$ we know that :

$I_{i} = m r_{i}^2$

$\textbf{The moment of inertia of the sun after it collapses }$ we know that :

$I_{f} = m r_{f}^2$

And we know that :

$T = \dfrac{2 \pi}{\omega} \quad \rightarrow \quad \omega_{i} = \dfrac{ 2\ \pi }{T_{i}} = {2\ \pi }{28 }$

So ,

$\begin{gather*} I_{i} \omega_{i} = I_{f} \omega_{f} \\ I_{i} \dfrac{2\ \pi }{T_{i} } = I_{f} \dfrac{2\ \pi }{T_{f} } \\ T_{f} = 2 \ \pi I_{f} \cdot \dfrac{ T_{i} }{2\ \pi I_{i}}\\ T_{f} = \dfrac{ T_{i} I_{f}}{I_{i}} \end{gather*}$

## Recommended textbook solutions #### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th EditionISBN: 9780133942651 (8 more)Randall D. Knight
3,508 solutions #### Mathematical Methods in the Physical Sciences

3rd EditionISBN: 9780471198260 (1 more)Mary L. Boas
3,355 solutions #### Fundamentals of Physics

10th EditionISBN: 9781118230718 (3 more)David Halliday, Jearl Walker, Robert Resnick
8,971 solutions #### University Physics, Volume 1

1st EditionISBN: 9781938168277Jeff Sanny, Samuel J Ling, William Moebbs
1,471 solutions