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.
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Given
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Derived Formulas (to know)
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v=(2πr)/T
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Fc=(mv2)/2=(4π2rm)/T2
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ac=(v2)/r
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Torb=(2πr3/2)/√(GM)
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FG=(GMm)/r2
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Etotal=-GMm/2r
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Ep=-(GMm)/r
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g=(GM)/r2
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ΔEp=GMm(1/rf-1/ri)
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vesc=√(2GM/r)
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vorb=√(GM/r)
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Fnet=Fc on any object undergoing uniform circular motion
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Vertical Circular Motion: over a hill, object swung with a string, loopty loop, etc.
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Top of swing: v = √(rg) → min. speed to maintain
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Bottom of swing: FT = (mv2)/r + mg → max. tension in the string
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Variable M → no motion object (i.e. Earth being orbited)
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Variable m → with motion object (i.e. satellite orbiting Earth)
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FN is present when an object is on the ground (i.e. car on a curve)
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Interstellar space station is in space → no gravity in space → only force is FN the apparent weight of something
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i.e. ... FG of person A due to person B → person A is being affected
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i.e. ... at 15500m above the surface of Earth → r = RE + 15500m
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If no ri mentioned → ri=∞
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If any final or initial variables are mentioned → ΣEi = ΣEf
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ET of any orbiting object in a gravitational field is always negative
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Geosynchronous: to move at the same speed as the Earth
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