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Circular Motion & Gravitation - Phy 12 - Unit 4 Cheat Sheet by

This cheat sheet summarizes key concepts, formulas, and problem-solving strategies for Circular Motion and Gravitation. It covers uniform circular motion, centripetal acceleration and force, Newton's Law of Universal Gravitation, orbital motion, and apparent weight in circular paths. It 's written based on how I was taught, so some variables or notation might differ slightly from other resources.

Formulas

Given
Derived Formulas (to know)
v=(2πr)/T
Fc=(mv2)/2=(4π2rm)/T2
ac=(v2)/r
Torb=(2πr3/2)/√(GM)
FG=(GMm)/r2
Etotal=-GMm/2r
Ep=-(GMm)/r
g=(GM)/r2
ΔEp=GMm(1/rf-1/ri)
vesc=√(2GM/r)
vorb=√(GM/r)
 

Key Concepts

Fnet=Fc on any object undergoing uniform circular motion
Vertical Circular Motion: over a hill, object swung with a string, loopty loop, etc.
Top of swing: v = √(rg) → min. speed to maintain
Bottom of swing: FT = (mv2)/r + mg → max. tension in the string
Variable M → no motion object (i.e. Earth being orbited)
Variable m → with motion object (i.e. satellite orbiting Earth)
 

To Remember

FN is present when an object is on the ground (i.e. car on a curve)
Inters­tellar space station is in space → no gravity in space → only force is FN the apparent weight of something
i.e. ... FG of person A due to person B → person A is being affected
i.e. ... at 15500m above the surface of Earth → r = RE + 15500m
If no ri mentioned → ri=∞
If any final or initial variables are mentioned → ΣEi = ΣEf
ET of any orbiting object in a gravit­ational field is always negative
Geosyn­chr­onous: to move at the same speed as the Earth
                                                   
 

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  • Published: 1st June, 2025

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