Rotating frames — centrifugal force, Coriolis force: Question bank

1.2.14 · D5 · Physics › Newton's Laws & Dynamics › Rotating frames — centrifugal force, Coriolis force

Shuru karne se pehle, do words jo confuse nahi karne:

Real force — kisi doosre object (haath, string, gravity, floor) se genuine push/pull. Har frame mein survive karta hai.
Fictitious force — ek bookkeeping term jo hum sirf isliye add karte hain kyunki hamara frame spin kar raha hai; iska koi source object nahi hota. Jaise hi inertial frame pe switch karo, gayab ho jaata hai.

Figure — Rotating frames — centrifugal force, Coriolis force

True or false — justify karo

True? Spinning carousel par chupchaap baitha ek body centrifugal force feel karta hai lekin zero Coriolis force.

True. Coriolis hai

- 2 m ω \times v_{rot}

; agar tum rotating frame mein rest par ho toh

v_{rot} = 0

isliye Coriolis vanish ho jaata hai, jabki centrifugal

- m ω \times (ω \times r)

sirf position par depend karta hai aur rehta hai.

True? Ek inertial (non-spinning) frame mein, centrifugal aur Coriolis dono forces zero hoti hain.

True. Ye rotating frame ke andar motion analyse karne ke artefacts hain; ek inertial observer ko koi extra terms nahi chahiye kyunki

F_{real} = m a

wahan khud kaam karta hai.

True? Coriolis force kisi particle ko speed up kar sakti hai.

False. Yeh hamesha

v_{rot}

ke perpendicular hoti hai, isliye

F_{Cor} \cdot v_{rot} = 0

aur yeh zero work karta hai — yeh sirf path ko bend karta hai, speed kabhi nahi badlata.

True? Centrifugal force kisi moving object par work kar sakti hai.

True. Yeh radially outward point karti hai, isliye agar object radially move kare toh force ka ek component motion ke saath hoga, nonzero work dega — Coriolis ke unlike yeh velocity ke perpendicular rehne par majboor nahi hai.

True? Spin rate

ω

double karne se centrifugal force double ho jaati hai.

False. Centrifugal magnitude hai

m ω^{2} r_{⊥}

(jahan

r_{⊥}

axis tak perpendicular distance hai), isliye yeh

ω^{2}

ke saath scale karta hai —

ω

double karne se yeh chaar guna badi ho jaati hai.

True? Spin rate

ω

double karne se (same

v_{rot}

ke saath) Coriolis force double ho jaati hai.

True. Coriolis magnitude hai

2 mω v_{rot} sin ϕ

(jahan

ϕ

ω

aur

v_{rot}

ke beech ka angle hai),

ω

mein linear hai, isliye double spin se double force milti hai.

True? Southern Hemisphere mein Coriolis force horizontally-moving air ko uske left taraf deflect karti hai.

True. Wahan

ω

zameen ke andar point karta hai, North ke relative

- 2 m ω \times v

ka sign flip kar deta hai, isliye cyclones counter-clockwise ki jagah clockwise ghoomte hain.

True? Equator par, horizontal motion ki Coriolis deflection zero hoti hai.

Mostly true — equator par

ω

ka vertical component vanish ho jaata hai, isliye horizontal winds ko wahan koi horizontal Coriolis turning nahi milti; ek horizontal

ω

component abhi bhi vertical motion ko deflect karta hai (dropped-ball case dekho).

True? Coriolis force mein 2 ka factor sirf ek convention hai jo

ω

mein absorb ho sakta hai.

False. Yeh physically acceleration expansion ke do alag

ω \times v_{rot}

terms se aata hai; ise absorb karna centrifugal term ko tod dega, jo single

ω

-squared carry karta hai.

Error dhundo

"Turn par tum bahar phenke jaate feel karte ho, toh ek real outward force tumhe push kar rahi hai." — error kahan hai?

Koi real outward force nahi hai. Sirf real force hai door/seat jo tumhe andar push kar raha hai; tumhara body seedha continue karna chahta hai, isliye turning car ke relative tum bahar drift karte ho aur ek fictitious "centrifugal" force ko blame karte ho.

"Coriolis force ke liye object ko bade radius par hona chahiye, kyunki yeh rotation effect hai." — error?

Coriolis

- 2 m ω \times v_{rot}

mein koi

r

hai hi nahi; yeh frame mein velocity par depend karta hai, position par nahi. Bilkul centre par ek object bhi Coriolis feel karta hai agar woh wahan move kar raha ho.

"Rotating frame mein rest par ek object koi fictitious forces feel nahi karta, kyunki woh move nahi kar raha." — error?

Woh abhi bhi centrifugal force feel karta hai, jo velocity nahi position par depend karta hai. Sirf Coriolis term switch off hoti hai jab

v_{rot} = 0

ho.

"Coriolis velocity ke perpendicular hone se path curve karta hai lekin centrifugal (radial) kabhi kuch curve nahi karta." — error?

Centrifugal zaroor motion alter karta hai — yeh radially outward push karta hai aur trajectory ka radial part change karta hai. "Speed change kiye bina curving" Coriolis ki special property hai, yeh statement nahi ki centrifugal inert hai.

F_{cf} = - m ω \times (ω \times r)

r

ke along point karta hai, isliye yeh hamesha origin se seedha bahar point karta hai." — error?

Yeh rotation axis se bahar point karta hai, origin se nahi. Sirf

r

ka woh component matter karta hai jo

ω

ke perpendicular hai, magnitude

m ω^{2} r_{⊥}

deta hai jahan

r_{⊥}

axis tak perpendicular distance hai.

"Humne fictitious forces Newton's second law fix karne ke liye invent kiye, isliye ye use violate karte hain." — error?

Ulta — ye non-inertial frame ke andar

F = m a

ko restore karte hain, exactly woh terms supply karke jo frame ki apni acceleration ne hata di thi. Kuch bhi violate nahi hota; hum bas frame ki motion ko forces ki tarah bookkeep karte hain.

Why questions

Kyun ek centrifugal (outward) force hoti hai lekin circular motion ki real physics ko centripetal (inward) force chahiye?

Inertial frame mein tumhe path ko circle mein bend karne ke liye ek real inward (centripetal) force chahiye; rotating frame mein, wahi requirement ek outward fictitious centrifugal force ke roop mein dikhti hai jo real inward force ko balance karta hai taaki object still lagta hai.

Kyun Coriolis force zero work karta hai jabki centrifugal force kar sakta hai?

Coriolis

ω \times v_{rot}

ke roop mein bana hai, isliye hamesha

⊥ v_{rot}

hai,

F \cdot v

zero kar deta hai. Centrifugal radially point karta hai aur uski koi aisi perpendicularity constraint nahi hai, isliye woh velocity ke saath direction share kar sakta hai.

Kyun Earth par ek phenke gaye baseball ke liye Coriolis effect negligible hai lekin hurricanes ke liye decisive?

Acceleration

2 ω_{\oplus} v

per second bahut chhota hai (

\sim 1 0^{- 3} m/s^{2}

), isliye ek ball ki short flight mein yeh imperceptible hai; weather system ke ghanton aur saikdon kilometres mein yeh ek dominant sideways turning mein accumulate ho jaata hai.

Kyun hum do-force result derive karte waqt

ω

ko constant maan lete hain, aur agar nahi hoti toh kya badlega?

Constant

ω

(

\dot{ω} = 0

) ek term drop kar deta hai; agar frame ki spin rate change ho, toh ek teesri fictitious force

- m \dot{ω} \times r

(Euler force) appear hoti hai — ek tangential kick jo tum tab feel karte ho jab carousel speed up ya slow down karta hai.

Kyun transport theorem ek plain multiple of

A

ki jagah cross product

ω \times A

produce karta hai?

Rigid rotation sirf ek vector ko reorient karta hai, uska tip ek circle ke saath sweep karta hai; us sideways sweep ki instantaneous rate exactly

ω \times A

hai, jo

A

ke perpendicular hai — ek plain scalar multiple galat tarike se vector ko khud ke along stretch kar deta.

Kyun Foucault Pendulum ka slow plane-rotation Earth ki spin ka evidence hai gravity ka nahi?

Uska swing plane isliye ghoomta hai kyunki Coriolis har swing mein bob ko sideways nudge karta hai; sirf ek rotating frame hi woh steady precession produce karta hai, isliye uski measurable turning rate

ω_{\oplus}

ki direct fingerprint hai.

Edge cases

Agar

v_{rot}

exactly

ω

ke parallel ho (spin axis ke seedha along motion), toh Coriolis force kya hai?

Zero, kyunki

ω \times v_{rot} = 0

jab vectors parallel hon (

sin ϕ = 0

) — axis ke purely along motion ko koi Coriolis deflection nahi milti.

Agar ek particle exactly rotation axis par baitha ho (

r_{⊥} = 0

), toh centrifugal force kya hai?

Zero, kyunki

F_{cf}

ki magnitude

m ω^{2} r_{⊥}

hai; axis par bahar phenke jaane ke liye koi perpendicular distance hi nahi hai.

North Pole par, ek puck frictionless ice par horizontally slide karta hai — uske Coriolis behaviour describe karo.

Wahan

ω

vertical hai, isliye kisi bhi horizontal velocity ko poori Coriolis deflection right taraf milti hai, puck ko ek clockwise circle (ek inertial circle) mein curve karti hai jaise rotating Earth se dekha jaye.

Agar

v_{rot}

ki direction reverse kar do toh Coriolis force ka kya hoga?

Yeh sign flip kar leti hai, kyunki

F_{Cor} = - 2 m ω \times v_{rot}

v

mein linear hai — apni motion reverse karne se sideways push reverse ho jaata hai, isliye bahar jaati aur andar aati hawa opposite taraf deflect hoti hai.

ω \to 0

(frame spinning band) ki limit mein, dono fictitious forces ka kya hoga?

Dono vanish ho jaati hain — Coriolis linearly aur centrifugal quadratically

ω

mein — ordinary inertial-frame Newton's law

F_{real} = m a

recover karta hai, bilkul expected ki tarah.

Equator par ek tower se giraaye gaye ball ke liye, kyun woh seedha neeche ki jagah thoda east mein girta hai?

Uski downward velocity Earth ki spin ke saath cross hoti hai isliye

- 2 m ω \times v

east point karta hai; fictitious deflection fall ko plumb line ke east taraf nudge karti hai, ek real, measured effect.

Recall Ek-line summary jo tumhe recite karni chahiye

Centrifugal = position-based, axis se outward, $\propto ω^{2} r_{⊥}$ , work kar sakta hai; Coriolis = velocity-based, motion ke perpendicular, $\propto ω v$ , zero work karta hai — aur dono inertial frame mein vanish ho jaate hain.