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Concept · Mechanics
Circular motion & gravitation
uniform circular motion (v, ω, T, f), centripetal acceleration v2/r=ω2·r and force, universal gravitation F=GMm/r2, gravity provides centripetal force, orbital/first-cosmic velocity, satellite period-radius (Kepler), surface g=GM/R2
Switches you to Physics
Named traps
17 ways this goes wrong.
Each is a named misconception the questions are built to catch. Open one for the move that tempts, and the fix.
- Centripetal force is an extra forceAdds centripetal force as a separate force on the free-body diagram instead of identifying it as the net of real forces.→
- Centripetal force points outwardDirects the centripetal (net) force outward, away from the center, instead of toward it.→
- Escape velocity depends on object massBelieves the escape (cosmic) velocity from a planet depends on the escaping object's mass.→
- Field strength uses orbiting massIncludes the satellite's mass in g=GM/r2, where only the central body's mass M appears.→
- Gravity as 1/r not 1/r2Uses an inverse-distance (1/r) dependence for gravitational force or field instead of inverse-square (1/r2).→
- Higher orbit means fasterBelieves a satellite in a higher orbit moves faster, contradicting v=√GM/r.→
- Kepler period-radius relation wrongUses a linear T proportional to r relation instead of T2 proportional to r3.→
- Min speed at top ignores gravityFinds the minimum speed at the top of a vertical loop without letting gravity supply the centripetal force.→
- Momentum unchanged in circular motionClaims momentum is constant in uniform circular motion because speed is constant, ignoring its changing direction.→
- No acceleration at constant speedConcludes acceleration is zero in uniform circular motion because the speed is constant, ignoring the direction change.→
- No gravity in orbitAsserts there is no gravity on an orbiting satellite/astronaut, rather than gravity providing the centripetal force.→
- Orbit radius used for surface gSubstitutes the orbital radius into surface g=GM/R2 instead of the planet's radius R.→
- Period/frequency invertedUses T=f instead of T=1/f, or otherwise inverts the period-frequency relationship.→
- Satellite mass kept in vKeeps the satellite's mass in the orbital-speed result, missing that v=√GM/r is independent of it.→
- Tension max at top of vertical circleAssumes string tension is greatest at the top of a vertical circle rather than at the bottom.→
- v and ω relation wrongConfuses v=ω·r, using ω/r or ω·r2, or otherwise mixes angular and linear quantities.→
- v2/r vs ω2 r confusedMismatches the centripetal acceleration formula, e.g. uses v2/r with ω, dropping or adding an r.→
Key formulas
No formula sheet is matched to this concept yet. Work it from first principles, and watch the traps.
Shaky underneath?
If the concept underneath still feels loose, patch it here before coming back to CSCA questions.
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