Answer in Mechanics | Relativity for Valentine Agun #108074

For a single rotating body, the law of conservation of momentum must be fulfilled. We will assume (which is a rough approximation) that the mass of the star is distributed evenly over its volume. Then the moment of inertia of the ball is written as “I=frac{2}{5}mR^2”, where m, R – its mass and radius [1]. the net angular momentum of a ball around a principal axis is “L=Iw”. When our Sun is normal star

(1) “L_o=frac{2}{5}M_{bigodot} R^2 cdot w_o”

After it collapses into a white dwarf, losing about half its mass in the process and winding up with a radius 1.0% (=0.01) of its existing radius the angular momentum will be

(2) “L_1=frac{2}{5}frac{M_{bigodot}}{2} (0.01cdot R)^2 cdot w_1”

According the law of conservation angular momentum (the lost mass carries away no angular momentum) we have “L_1=L_o” . Thus for new angular velocity “w_1” we have

(3) “frac{2}{5}frac{M_{bigodot}}{2} (0.01cdot R)^2 cdot w_1=frac{2}{5}M_{bigodot} R^2 cdot w_o\nw_1=2 cdot 100^2 w_o=2cdot 10^4 w_o”

“w_o=frac{2pi}{30 day}=frac{2pi}{30cdot 24cdot 60cdot 60 s}=2pi cdot 3.9cdot 10^{-7} s^{-1}” Finally for new rotation we get

“w_1=2pi cdot 7.8cdot 10^{-3} s^{-1}” Thus our Sun’s white dwarf will rotate with period “T=frac{1}{7.8cdot 10^{-3}}s=128s”

The KE we can find by the equation

“E_k=frac{Iw^2}{2}=frac{Lw}{2}” Initial KE is “E_o=frac {L_ow_o}{2}”. The final KE is “E_1=frac {L_1w_1}{2}”. We can find a relationship

(4) “frac {E_1}{E_o}=frac {L_1 w_1}{L_ow_o}=frac {w_1}{w_o}=2cdot 10^4”

Where we taken into account the law of conservation angular momentum and (3). In our assumptions, the gravitational potential energy of the Sun’s mass is completely converted into the kinetic energy of rotation of its remainder.

Answer: The Sun’s new rotation period will be about 128 s. The  KE of white dwarf will exceed the initial value for the Sun by “2cdot 10^4” times.


Calculate the price
Make an order in advance and get the best price
Pages (550 words)
*Price with a welcome 15% discount applied.
Pro tip: If you want to save more money and pay the lowest price, you need to set a more extended deadline.
We know how difficult it is to be a student these days. That's why our prices are one of the most affordable on the market, and there are no hidden fees.

Instead, we offer bonuses, discounts, and free services to make your experience outstanding.
How it works
Receive a 100% original paper that will pass Turnitin from a top essay writing service
step 1
Upload your instructions
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
Pro service tips
How to get the most out of your experience with TheBestPaperWriters
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
See why 20k+ students have chosen us as their sole writing assistance provider
Check out the latest reviews and opinions submitted by real customers worldwide and make an informed decision.
English 101
Very good job. I actually got an A
Customer 452443, September 25th, 2022
Business Studies
Job well done. Finish paper faster than expected. Thank you!
Customer 452451, October 3rd, 2022
excellent loved the services
Customer 452443, September 23rd, 2022
Business Studies
Excellent service - thank you!
Customer 452469, February 20th, 2023
Job well done and completed in a timely fashioned!
Customer 452451, November 18th, 2022
Architecture, Building and Planning
The assignment was well written and the paper was delivered on time. I really enjoyed your services.
Customer 452441, September 23rd, 2022
Public Administration
Excellent timely work
Customer 452451, April 19th, 2023
The paper was EXCELLENT. Thank you
Customer 452449, September 23rd, 2022
Thanks a lot the paper was excellent
Customer 452453, October 26th, 2022
Excellent services will definitely come back
Customer 452441, September 23rd, 2022
Business Studies
Thank you!
Customer 452451, November 27th, 2022
Customer reviews in total
Current satisfaction rate
3 pages
Average paper length
Customers referred by a friend
15% OFF your first order
Use a coupon FIRST15 and enjoy expert help with any task at the most affordable price.
Claim my 15% OFF Order in Chat