Motion Of Centre Of Mass
Chapter Name : System Of Particles And Rotational Motion |
Sub Topic Code : 101_11_07_03_01 |
Topic Name : Motion Of Centre Of Mass |
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Sub Topic Name : Motion Of Centre Of Mass |
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Introduction
What is the application and importance of inventing the concept of Center of Mass?
Pre-Requisites:
Concept of rigid body, particle, center of mass and its mathematical expressions. Newton’s Laws of motion and basics of vector and its algebra.
Activity:
Suppose you are running with a ball or a bag in your hand. And then while running you throw it in some direction. Then you will observe that you experience a “jerk” or a “force” or a “resistance” in the direction directly opposite in which the object was thrown. So, WHY do you feel so? The answer lies in this awesome concept.
Real Life Question:
When the Brahmos Missile of India fails in its test by breaking into one or many parts in mid-air, then is there any way to calculate where the other parts will fall provided you have information of one part only?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Center Of Mass Internal And External Forces | It is the weighted average location of all the mass in a body or a group of bodies. There is a mathematical expression for finding the Center of Mass of discrete no. of particles as well as for continuous bodies. Internal Forces as the name says are the forces which arise due to the interactions among the particles itself. On the other hand, external forces are those which are applied by the bodies outside the system. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| A bat or a baseball bat or a maybe a pen | Just project it some angle. The object will move in a “dis-orderly” fashion which will not allow you to define the trajectory clearly. But surprisingly, the Center of mass of moves in a parabolic shape. So, essentially we realize that instead of analyzing the motion of each particle of a continuous body, it is best to analyse the center of mass and hence its motion. |
Real life uses :
Helps to apply the concept of center of mass to real life based problems. Has lots of applications.
Places to visit :
Your home or surroundings having some rigid body. A rigid body will be really good to visualize what exactly this concept is all about. For example a bag, bat etc.
Practical examples around us
| Examples | Explainations |
|---|---|
| If possible try walking on a log floating in water. You will observe that as you walk you, the log also moves, i.e. it has some motion. And you will observe that the motion is specific. So, can you find how much the log moved? | The beauty lies in the fact that there are no external forces acting on the “log + you” as a system. Hence according to the concept of “motion of center of mass”, your center of mass should remain at rest. Hence, using this simple fact you can calculate the distance moved by the log as you walked. |
What you learn in Theory:
How mathematically Center of Mass helps to simplify the problem by changing “many” to just “one” particles.
What you learn in Practice:
The importance of the concept of Center of mass and its practical utility. And also the fact that it is easy to focus and analyze the motion of center of mass rather than considering each and every particle of the body. This has a variety of applications.