1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kifflom [539]
3 years ago
13

Show that rigid body rotation near the Galactic center is consistent with a spherically symmetric mass distribution of constant

density.
Physics
1 answer:
irakobra [83]3 years ago
6 0

To solve this problem we will use the concepts related to gravitational acceleration and centripetal acceleration. The equality between these two forces that maintains the balance will allow to determine how the rigid body is consistent with a spherically symmetric mass distribution of constant density. Let's start with the gravitational acceleration of the Star, which is

a_g = \frac{GM}{R^2}

Here

M = \text{Mass inside the Orbit of the star}

R = \text{Orbital radius}

G = \text{Universal Gravitational Constant}

Mass inside the orbit in terms of Volume and Density is

M =V \rho

Where,

V = Volume

\rho =Density

Now considering the volume of the star as a Sphere we have

V = \frac{4}{3} \pi R^3

Replacing at the previous equation we have,

M = (\frac{4}{3}\pi R^3)\rho

Now replacing the mass at the gravitational acceleration formula we have that

a_g = \frac{G}{R^2}(\frac{4}{3}\pi R^3)\rho

a_g = \frac{4}{3} G\pi R\rho

For a rotating star, the centripetal acceleration is caused by this gravitational acceleration.  So centripetal acceleration of the star is

a_c = \frac{4}{3} G\pi R\rho

At the same time the general expression for the centripetal acceleration is

a_c = \frac{\Theta^2}{R}

Where \Theta is the orbital velocity

Using this expression in the left hand side of the equation we have that

\frac{\Theta^2}{R} = \frac{4}{3}G\pi \rho R^2

\Theta = (\frac{4}{3}G\pi \rho R^2)^{1/2}

\Theta = (\frac{4}{3}G\pi \rho)^{1/2}R

Considering the constant values we have that

\Theta = \text{Constant} \times R

\Theta \propto R

As the orbital velocity is proportional to the orbital radius, it shows the rigid body rotation of stars near the galactic center.

So the rigid-body rotation near the galactic center is consistent with a spherically symmetric mass distribution of constant density

You might be interested in
In each cylinder, draw the piston and the gas particles based on the temperature shown.
tangare [24]
I need more information
8 0
2 years ago
Which sentence uses a verb incorrectly?
Burka [1]

Answer:

The answer is B).

Explanation:

The correct way to write this sentence is: After I woke up this morning, I got me a tall glass of orange juice.

5 0
3 years ago
the atoms in a sample are close together but can slide past one another. as the atoms lose energy, they move slower. the atoms b
frosja888 [35]
The change of state that is occurring is from the liquid state to the solid state.
8 0
3 years ago
Read 2 more answers
Oil and gas were formed millions of years ago from what
loris [4]
Over millions of years, layer after layer of sediment and other plants and bacteria were formed. ... Even higher heat or biomass made predominantly of plant material produced natural gas.
3 0
3 years ago
If the electron has half the speed needed to reach the negative plate, it will turn around and go towards the positive plate. Wh
In-s [12.5K]

Answer:

 v = -v₀ / 2

Explanation:

For this exercise let's use kinematics relations.

Let's use the initial conditions to find the acceleration of the electron

            v² = v₀² - 2a y

when the initial velocity is vo it reaches just the negative plate so v = 0

           a = v₀² / 2y

now they tell us that the initial velocity is half

          v’² = v₀’² - 2 a y’

          v₀ ’= v₀ / 2

at the point where turn v = 0              

          0 = v₀² /4  - 2 a y '

          v₀² /4 = 2 (v₀² / 2y)  y’

          y = 4 y'

          y ’= y / 4

We can see that when the velocity is half, advance only ¼ of the distance between the plates, now let's calculate the velocity if it leaves this position with zero velocity.

         v² = v₀² -2a y’

         v² = 0 - 2 (v₀² / 2y) y / 4

         v² = -v₀² / 4

         v = -v₀ / 2

We can see that as the system has no friction, the arrival speed is the same as the exit speed, but with the opposite direction.

7 0
3 years ago
Other questions:
  • The base unit prefix used for 1,000× is _____. kilo milli centi deka
    10·1 answer
  • The weight of air measured in units of force per area is called _____.
    6·2 answers
  • If you use such a tank to fill 0.020 m3 foil balloons (which don't stretch, and so have an internal pressure that is very close
    7·1 answer
  • What is the frequency of a wave that has a speed of 0.6 m/s and a wavelength of 0.020 meter?
    14·1 answer
  • The apartment’s explosion, reportedly caused by a gas leak, produced a violent release of gas and heat. The heat increased the _
    12·2 answers
  • Application of pressure​
    5·1 answer
  • The insulating solid sphere in the previous Example 24.5 has the same total charge Q and radius a as the thin shell in the examp
    9·1 answer
  • ____________ is considered one of the great geniuses and gave us the formula, E=mc2.
    15·2 answers
  • Six automobiles are initially traveling at the indicated velocities. The automobiles have different masses and velocities. The d
    15·1 answer
  • During the course of a concert, the temperature of a pipe organ gradually increases. As a result, the frequency of the sound fro
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!