# Collision of 2 Stars: Calculating Angular Velocity & Momentum

• Gogsey
In summary, the conversation discusses the scenario of two spherical stars colliding, where one star is stationary and the other has a velocity. Both stars have uniform density and merge instantly upon contact. The question at hand is to calculate the angular velocity and angular momentum of the final star. The moment of inertia of a sphere is mentioned and the possibility of the larger star spinning on its axis is considered. The concept of linear and angular momentum is brought up and the idea of the smaller star's initial path and impact parameter is discussed. The conservation of angular momentum is also mentioned.
Gogsey
So the question is basically,

A stationary spherical star sits at the origin, and has mass 8M and radius 2R. Another sphere of mass M and radius R has a velocity and is coming toward the larger mass. We are to neglect gravitational effect until the 2 masses come into contact. What happens is that the edge of each mass comes into contact and the combine the make an even larger star. Both maases are to be treated as spherical liquid state objects with uniform density before and after the collision. When they come into contact they merge instantly. We are to calculate the angular velocity and angular momentum of the final star.

So the moment of inertia of a sphere is 2/5 MR^2.

Trouble is that is the larger star spinning on its axis? If it is then angular momentum should be 64/5 MR^2, if we take the smaller sphere to be the unit sphere. If not, then its angualr momentum should be zero, right?

Also, I'm assuming if gravity has no effect, then the path should be a straight line, right?

It seems like bfore the collision is linear momentum, and after the collision is angular momentum. How can you equate linear and angular momentum?

Was the smaller star originally traveling along a line connecting the centers, or was it traveling along a line that was offset, so there is an impact parameter (the perpendicular distance between the center of the largest star and the approach path of the smaller star when the smaller star was far away.)

Remember angular momentum has to be conserved.

## 1. What is angular velocity?

Angular velocity is a measure of the rate at which an object rotates or spins around an axis. It is typically measured in radians per second (rad/s) or degrees per second (deg/s).

## 2. How is angular velocity calculated?

Angular velocity is calculated by dividing the change in the object's angle (in radians or degrees) by the change in time (in seconds). The formula for angular velocity is ω = Δθ/Δt, where ω is angular velocity, Δθ is the change in angle, and Δt is the change in time.

## 3. What is momentum?

Momentum is a measure of an object's motion and is calculated by multiplying its mass by its velocity. It is a vector quantity, meaning it has both magnitude and direction.

## 4. How is momentum calculated?

Momentum is calculated by multiplying an object's mass by its velocity. The formula for momentum is p = mv, where p is momentum, m is mass, and v is velocity.

## 5. How does the collision of two stars affect their angular velocity and momentum?

The collision of two stars can significantly impact their angular velocity and momentum. The two stars will experience a change in their angular velocity due to the transfer of rotational energy during the collision. Depending on the angle and speed of the collision, the stars' momentum can also change, potentially causing them to move in a different direction or at a different speed after the collision.

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