Dosto bahut sare student ke man me yah sabal aata hai ki "What is center of mass?" Aaj ham is question ko acche se jan lege ki center of mass kya hota hai? Agar aap center of mass ke bare me nhi jante hai to is post ke bad aap acche se jan jaieaga ki center of mass kya hota hai?
(1) Formulae for discrete system:-
Sabse pahle to hame yah jan lena chahiea ki yah discrete system hota kya hai? Agar ham system me bartmaan sare body ko ya uske particle ko count kar sake to ise discrete system kha jata hai. Jab aapka system of body discrete ho to us time simple formulae ki jarurat hoti hai. Is time system ke body ke mass aur co-ordinate ke product ka sum hota hai aur total sum me system ke mass se divide karte hai. aap formulae ko niche se dekh sakte hai.
(2) Formulae for regular system:-
Regular system ek aisa body ya system ko kha jata hai jiske particle ko ham count nhi kar sakte hai. Example:- Rod, Disc, Sphere. Jab bhi center of mass regular system ka calculate karna hota hai to iske lie hame technique of integration ki jarurat padti hai. Integration ke help se hi ham us system ka center of mass calculate kar sakte hai. Is method me ek bahut chota sa mass dm liya jata hai. is chote se mass ke sath integration ka technique apply kiya jata hai. aap niche ke formulae se acche se center of mass calculate kar sakte hai.
What is center of mass? (Center of mass kya hai?)
Sabse pahle to yah janna jaruri hai ki center of mass hota kya hai? Aap sabse easy me samajhiea ki center of mass ek aisa point hota hai jha par whole system ke mass ko concentrated mana ja sakta hai. Bahut bar numerical solve karte time system ke mass ko ek bindu par concentrated man ne jarurat hoti hai. Islie center of mass ka concept aata hai.Why center of mass required?
Sabse pahle to ham yah janege ki center of mass ki hame jarurat kyo padtee hai? Actually Newton's laws of motion chapter ke pahle ham jo bhi study karte hai bah total study point object ke lie sahi hota hai islie jab hame study Newton's laws of motion ke bad karni hoti hai tab hame centre of mass ki jarurat padtee hai kyonki NLM ke bad jo study karni hoti hai bah ek rigid body ke lie hoti hai. Is time jo bhi Newton ka formulae point object ke lie bna hota hai use ham ek rigid body par apply karne ke lie centre of mass ki study karte hai. Jab kisi body ke mass ko ek centre par concentrated mana jata hai tab bah body ek point mass ke tarah work karta hai. Ab aap acchi tarah se samajh rhe hoge ki centre mass ka requirement kyo hoti hai?How center mass can be calculated?
Center of mass calculate karne ka kuch method hota hai. In sare mathod me 2 method bahut hi jyada famous hai. Formulae apply karne se pahle yah bhi dekhna hota hai ki system discrete hai ya regular. Agar system discrete hai to uske lie alag formulae aur agar system regular hai to uske lie alag formulae hota hai.(1) Formulae for discrete system:-
Sabse pahle to hame yah jan lena chahiea ki yah discrete system hota kya hai? Agar ham system me bartmaan sare body ko ya uske particle ko count kar sake to ise discrete system kha jata hai. Jab aapka system of body discrete ho to us time simple formulae ki jarurat hoti hai. Is time system ke body ke mass aur co-ordinate ke product ka sum hota hai aur total sum me system ke mass se divide karte hai. aap formulae ko niche se dekh sakte hai.
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| How to Calculate center of mass. |
Regular system ek aisa body ya system ko kha jata hai jiske particle ko ham count nhi kar sakte hai. Example:- Rod, Disc, Sphere. Jab bhi center of mass regular system ka calculate karna hota hai to iske lie hame technique of integration ki jarurat padti hai. Integration ke help se hi ham us system ka center of mass calculate kar sakte hai. Is method me ek bahut chota sa mass dm liya jata hai. is chote se mass ke sath integration ka technique apply kiya jata hai. aap niche ke formulae se acche se center of mass calculate kar sakte hai.
Center of mass of different bodies:-
- Agar aapka body ek uniform rod ho to uska center of mass rod ke middle point par hota hai.
- Agar body uniform ring ho to uska center of mass body ke centre par hota hai.
- Uniform disck ke lie bhi center of mass uske center par hota hai.
- Uniform sphere (hollow or solid) ka bhi center of mass uske center par hota hai.
- Agar aapke uniform solid cone ho to iska center of mass base se h/4 par ya vertex se 3h/4 par hota hai.
Important point about Center of mass:-
- Agar koi body non-uniform ho to uska center of mass body ke bhari part ki or shift karta hai.
- Kisi body ka center of mass us body ke outside bhi ho sakta hai.
- Center of mass ka matlab yah nhi hota hai ki body ka mass sirf ek hi point par concentrated hai.
- Center of mass ek hypothetical point hota hai jha par sare mass ko concentrated mana ja sakta hai.
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