Define momentum
Scenario
Agar ek halki table-tennis ball tumhe thodi speed se hit kare toh chot nahi lagti. Lekin agar ek bullet aakar hit kare, jiska mass table-tennis ball se kam bhi ho sakta hai, toh woh bahut nuqsaan phucha sakti hai kyunki uski speed bohot zyada hai.
Sirf mass ya sirf speed se impact pata nahi chalta, toh impact ki taqat kis physical quantity par depend karti hai?
Mental model
Momentum kisi chalti hui cheez ke 'power of motion' ko measure karta hai. Yeh mass aur speed dono ka combine effect hai.
Momentum ek combination hai. Koi object kitna bhari hai aur kitni tez chal raha hai, in dono ka product humein batata hai ki usko rokna kitna mushkil hoga. Heavier cheez slow chal rahi ho, ya light cheez fast chal rahi ho, dono ka momentum zyada ho sakta hai.
Explanation
Newton ne jab force aur motion ki deeply study ki, toh unhe realize hua ki kisi chalti hui cheez ka impact sirf uske mass ya sirf uski velocity par depend nahi karta, balki dono ke combination par depend karta hai. Unhone ek nayi quantity introduce ki jise 'momentum' kaha gaya.
Momentum ko letter `p` se denote kiya jata hai. Mathematically, kisi object ka momentum uske mass `m` aur uski velocity `v` ke product ke equal hota hai. Iska formula hai `p = m * v`. Is equation se clear hai ki agar kisi object ka mass zyada hai ya uski velocity zyada hai, toh uska momentum automatically zyada ho jayega.
Kyunki velocity ek vector quantity hai (yani usme magnitude aur direction dono hote hain), isliye momentum bhi ek vector quantity hai. Momentum ki direction hamesha wahi hoti hai jo velocity ki hoti hai. Agar car north ki taraf ja rahi hai, toh uski momentum ki direction bhi north hi hogi.
Momentum ki SI unit dhoondhna bohot aasaan hai. Mass ko kilograms (`kg`) mein aur velocity ko meters per second (`m/s`) mein measure karte hain. Toh momentum ki unit ho gayi `kg * m/s`. Ek aur interesting cheez: agar koi object rest par hai, yani uski velocity zero hai, toh chahe uska mass kitna bhi ho, uska momentum zero hi hoga.
Worked example
Problem: Calculate the momentum of a toy car of mass `200 g` moving with a velocity of `5 m/s`.
- Sabse pehle mass ko SI unit yani kilogram (`kg`) mein convert karna zaroori hai. `1 kg = 1000 g`.
- Ab velocity ki value formula mein direct substitute karo: `p = m * v`.
- Final multiplication solve karo.
Answer: The momentum of the toy car is `1.0 kg m/s`.
Problem: An elephant of mass `3000 kg` is running east at a velocity of `4 m/s`. What is its momentum?
- Humein mass aur velocity dono exact SI units mein diye gaye hain, toh sidhe multiply karna hai.
- Momentum calculate karo.
- Kyunki momentum ek vector quantity hai, direction specify karna important hai.
Answer: The momentum of the elephant is `12000 kg m/s` due east.
Key points
- Formula: Momentum (`p`) = mass (`m`) × velocity (`v`).
- Vector Quantity: It has both magnitude and direction. The direction of momentum is the same as the direction of velocity.
- SI Unit: The SI unit of momentum is kilogram-meter per second (`kg m/s`).
Common mistakes
- Forgetting to convert mass to kilograms: Kayi baar questions mein mass grams mein diya hota hai. Agar directly multiply kar diya bina `kg` mein convert kiye, toh momentum ka result galat unit (`g m/s`) mein aa jayega, jo standard nahi hai.
Recall questions
- Is momentum a scalar or a vector quantity?
- What is the momentum of an object of mass `m` moving with a velocity `v`?
- What is the momentum of an object that is at rest?
- How does momentum change if the velocity of an object is doubled while its mass remains constant?
Questions & answers
Write the mathematical formula for momentum and state its SI unit.
The formula is `p = mv`. The SI unit is `kg m/s`.
Approach: Simply state the formula relating momentum to mass and velocity, and derive the unit from their standard SI units.
Calculate the momentum of a `5 kg` object moving at `2 m/s`.
`10 kg m/s`.
Approach: Multiply mass and velocity.
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