Linear Momentum Of A System Of Particles
Chapter Name : System Of Particles And Rotational Motion |
Sub Topic Code : 101_11_07_04_01 |
Topic Name : Linear Momentum Of A System Of Particles |
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Sub Topic Name : Linear Momentum Of A System Of Particles |
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Introduction
If the motion of a body can be described in terms of a single point, center of mass, then does the momentum also follow the same path?
Pre-Requisites:
Newton’s Law of motion, motion of center of mass and its mathematical expression, concept of a particle and internal and external forces.
Activity:
The exploding of a bomb into fragments and how exactly this “phenomenon” is involved in the linear momentum of center of mass concept.
Real Life Question:
A bomb exploded into many pieces. Then can we somehow calculate the velocity and the direction in which some of the pieces flew?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| System of particles Linear Momentum | It is nothing but a collection of discrete particles. It is defined as the product of mass and velocity of a particle or an object. It is a vector quantity and a very important one too! It is associated with Newton’s second law of motion through the equation F = dp/dt, where both momentum (p) and force (F) are vectors. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| A toy gun | When you shoot a target using this toy gun, then you feel a “backward” impact on your hand. Why is this? This is because initially the “gun+bullet (or anything)” as a system are at rest and therefore according to this concept the initial momentum is 0 therefore after firing also it should be 0 too. Hence, the “backward” motion to conserve the linear momentum of the center of mass of the system as no external force. |
Real life uses :
Helps to amplify the applications of Newton’s laws of motion by integrating center of mass along with it.
Places to visit :
A library. Try reading on “Binary Stars”. It’s a beautiful application of this concept taking place way beyond the 4 walls of the classroom!
Practical examples around us
| Examples | Explainations |
|---|---|
| Suppose you have a rod and you throw it in the air. The momentum of the rod will be how much? | If you try to attempt to calculate the momentum of the rod using “JUST” the Newton’s Laws of motion, then think again! It’s not one particle. Rod is a collection of many particles. Then how can you apply the laws and find the momentum? This can be done if you know that what is a center of mass and how to analyze its motion. Then consequently you can write the momentum of the rod in terms of center of mass using this concept. |
What you learn in Theory:
The mathematical way of expressing Newton’s law of motion in terms of a center of mass.
What you learn in Practice:
How Newton’s Law of motion can be applied to objects in our surroundings using the application of motion of center of mass.