course_planning:course_notes:momentum_principle

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course_planning:course_notes:momentum_principle [2014/07/08 02:33] – caballerocourse_planning:course_notes:momentum_principle [2014/07/17 12:43] (current) – [The Momentum Principle] caballero
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 ==== The Momentum Principle ==== ==== The Momentum Principle ====
  
-The Momentum Principle is one of three fundamental principles of mechanics. No matter what system you choose the Momentum Principle, which is also known as [[|http://en.wikipedia.org/wiki/Newton's_laws_of_motion#Newton.27s_2nd_Law|"Newton's Second Law of Motion"]], will correctly predict the motion of that system. It is the quantitative form of Newton's First Law; it tells you precisely how the momentum (and thus the velocity) of an system will evolve when it experiences a net force. +The Momentum Principle is one of three fundamental principles of mechanics. No matter what system you choose the Momentum Principle, which is also known as [[http://en.wikipedia.org/wiki/Newton's_laws_of_motion#Newton.27s_2nd_Law|"Newton's Second Law of Motion"]], will correctly predict the motion of that system. It is the quantitative form of Newton's First Law; it tells you precisely how the momentum (and thus the velocity) of an system will evolve when it experiences a net force. 
  
 If a system experiences a net force, it can experience either: If a system experiences a net force, it can experience either:
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 If you divide both sides by this time interval ($\Delta t$) and take the limit as the time interval goes to zero, ($\Delta t \rightarrow 0$), you obtain the exact definition of the net force acting on the system at any instant, If you divide both sides by this time interval ($\Delta t$) and take the limit as the time interval goes to zero, ($\Delta t \rightarrow 0$), you obtain the exact definition of the net force acting on the system at any instant,
  
-$$F_{net} = \dfrac{d\vec{p}}{dt}$$+$$\vec{F}_{net} = \dfrac{d\vec{p}}{dt}$$
  
 ==== Net Force ==== ==== Net Force ====
  
-**Force:** A vector that quantifies the interactions between two objects. +//A force is a vector that quantifies the interaction between two objects.// 
  
 There are two types of forces that you will work with in mechanics: gravitational forces and electrostatic forces. As you will learn, all interactions that you will consider in mechanics are a result of objects either having mass and, thus, attracting gravitationally, or being charged, and thus, interacting through electrical repulsion or attraction. There are two types of forces that you will work with in mechanics: gravitational forces and electrostatic forces. As you will learn, all interactions that you will consider in mechanics are a result of objects either having mass and, thus, attracting gravitationally, or being charged, and thus, interacting through electrical repulsion or attraction.
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 Systems might interact with several objects in their surroundings, and thus, experience a variety of forces. Fortunately to make predictions of the motion, the Momentum Principle only requires you know the net force. Systems might interact with several objects in their surroundings, and thus, experience a variety of forces. Fortunately to make predictions of the motion, the Momentum Principle only requires you know the net force.
  
-**Net Force:**: The vector sum of all forces acting (at an instant) on a system as due to the systems' surroundings.+//The net force is the vector sum of all forces acting (at an instant) on a system as due to the systems' surroundings.//
  
 Mathematically, we can represent this sum using vector notation: Mathematically, we can represent this sum using vector notation:
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 where each interaction/force (at an instant) is counted as a specific $\vec{F}_{i}$. where each interaction/force (at an instant) is counted as a specific $\vec{F}_{i}$.
  
-**Impulse:** The product of a force and a time interval over which that force acts, which is mathematically equivalent to the change in momentum (Impulse $\equiv \vec{F} \Delta t$).+//The impulse is the product of a force and a time interval over which that force acts//, which is mathematically equivalent to the change in momentum (Impulse $\equiv \vec{F} \Delta t$).
  
 Sometimes, you might find it useful to think about the impulse applied to a system as being responsible for the change in momentum of the system. An impulse may be calculated for each force (e.g., //impulse delivered by the gravitational force//) or the total force (i.e., //the "net" impulse applied to the system//). Sometimes, you might find it useful to think about the impulse applied to a system as being responsible for the change in momentum of the system. An impulse may be calculated for each force (e.g., //impulse delivered by the gravitational force//) or the total force (i.e., //the "net" impulse applied to the system//).
    
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