Question

The stars, gas and dust in a galaxy rotate about the center of the galaxy. We would like to know exactly how to describe the rotation of all parts of the galaxy. In other words, we want to know if galaxies rotate like merry-go-rounds, or like planets orbit the Sun, or in some other way.

1. Do points near the center of a merry-go-round complete a full rotation in the same amount of time as points near the outer edge of the merry-go-round?

2. How does the distance traveled by a point near the center of a merry-go-round compare to the distance traveled by a point near the outer edge of the merry-go-round when they complete a full rotation?

3. Imagine you are on a rotating merry-go-round. Describe how your speed would change as you moved from standing at the center of a merry-go-round to the outer edge.

We know that the planets in our solar system all orbit the Sun. Furthermore, we know that the planets are all located at different distances from the Sun and from Kepler's 3rd Law we know that the planets have different orbital periods depending on their distances from the Sun.

4. How does the distance that a planet near the Sun travels in one complete orbit compare to the distance traveled in one complete orbit by a planet that is located far from the Sun?

If the planets all orbited the Sun with the same speed, then a planet located two times farther than Earth's distance from the Sun would have an orbital period exactly two times longer than Earth's orbital period.

5. The Earth orbits the Sun at a distance of 1 AU and takes 1 year to complete its orbit. Jupiter orbits the Sun at a distance of 5.2 AU and takes 11.9 years to complete its orbit. Which of these two planets orbits the Sun with the faster speed and which has the slower speed?

6. For our solar system, how do the speeds of the planets change as you move away from the Sun?

this is all the information that was given on my worksheet.

Answer 1

1) the points near the center of merry go round complete the full rotation in same time as compared to time taken by point near the outer edge. It is so because all the points in the system have same angular velocity.

2) the distance moved by point near the center of merry go round in one complete rotation is less than the distance moved by point near the outer edge , because circumference of outer edge is greater than the circumference of point near the center of merry go round.

3) as we move from center of merry go round , towards the outer edge , the moment of inertia increases and hence the angular velocity decreases because the angular momentum is to remain constant (angular momentum = moment of inertia× angular velocity).