Why is the specific angular momentum equal to this?

In summary, specific angular momentum is a fundamental quantity that describes the rotational motion of an object in physics. It is calculated by multiplying the angular velocity by the moment of inertia and is equal to the cross product of an object's position vector and its linear momentum. It differs from total angular momentum in that it takes into account the mass of the object. Additionally, specific angular momentum is conserved, meaning it remains constant unless acted upon by an external torque, which is a key principle in analyzing and predicting the behavior of rotating systems.
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From a wiki's vis-viva equation page, it is given that the specific angular momentum h is also equal to the following:

h = wr^2 = ab * n

How can ab * n be derived to be equal to the angular momentum using elliptical orbit energy/momentum/other equations without having to use calculus or equations involving eccentricity?
 
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  • #2
Oh... Wait. This is the old version of this. I understand how it works now. Could someone tell me how geometrically or algebraically you can derive b2 = ra * rb?
 

1. Why is specific angular momentum important in physics?

Specific angular momentum is important in physics because it is a fundamental quantity that describes the rotational motion of an object. It is a conserved quantity, meaning it remains constant unless acted upon by an external torque. This makes it a useful tool for analyzing and predicting the behavior of rotating systems.

2. How is specific angular momentum calculated?

Specific angular momentum is calculated by multiplying the angular velocity of an object by its moment of inertia. The formula for specific angular momentum is L = Iω, where L is specific angular momentum, I is moment of inertia, and ω is angular velocity. The units for specific angular momentum are kilogram meters squared per second (kg·m^2/s).

3. Why is the specific angular momentum equal to the product of moment of inertia and angular velocity?

This relationship is derived from the definition of angular momentum, which states that it is equal to the cross product of an object's position vector and its linear momentum. By substituting the equation for linear momentum (p = mv) and the equation for angular velocity (ω = v/r) into this definition, we arrive at the formula for specific angular momentum (L = Iω).

4. What is the difference between specific angular momentum and angular momentum?

Specific angular momentum (L) refers to the rotational momentum of an object per unit mass, while angular momentum (J) refers to the total rotational momentum of an object. In other words, specific angular momentum takes into account the mass of the object, while angular momentum does not. The units for angular momentum are kilogram meters squared per second (kg·m^2/s).

5. How does specific angular momentum relate to the conservation of angular momentum?

Specific angular momentum is a conserved quantity, meaning it remains constant unless acted upon by an external torque. This is known as the law of conservation of angular momentum. When there is no external torque acting on a system, the specific angular momentum of the system remains constant. This is a fundamental principle in physics and is used to analyze and predict the behavior of rotating systems.

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