Circular Motion and Gravitation: every key term you need (+ practice quiz)
24 flashcard terms for AP Physics 1 Unit 5, written to match the course framework. Read them here, drill them as flashcards, or take the 24-question quiz. Free, no account needed.
Object moves in circle at constant speed; velocity direction changes (constant acceleration). Centripetal acceleration a_c = v²/r.
Centripetal Force
Net force toward center. F_c = mv²/r = mω²r. Provides centripetal acceleration. Not a new force; gravity, tension, friction can provide.
Angular Velocity (ω)
Angular displacement per time. ω = v/r or ω = 2π/T where T = period.
Period & Frequency
Period T: time for one revolution. Frequency f: revolutions per time. f = 1/T. ω = 2πf.
Banking Angles
Road banked to reduce required friction. Normal force component provides centripetal force. Ideal angle: tan(θ) = v²/(rg).
Universal Gravitation
F_g = G·m₁m₂/r². Gravity acts between all masses. G = 6.67×10⁻¹¹ N·m²/kg². Weakest fundamental force.
Gravitational Field
g = F_g/m = GM/r². Acceleration on object due to mass M at distance r. At Earth surface: g ≈ 9.8 m/s².
Orbital Motion
Gravity provides centripetal force. GMm/r² = mv²/r → v = √(GM/r). Faster orbit = smaller r.
Orbital Velocity
v_orbit = √(GM/r). Kepler's Third Law: T² ∝ r³. Doubling r → √8× period.
Unit 5 Summary
Circular motion requires centripetal force (toward center). Gravity provides force for orbits. Orbital speed depends on distance from mass.
Centripetal Force Is Not a New Force
'Centripetal' names the role, not the source. Tension, gravity, friction, or a normal force supplies it. Never draw a separate 'centripetal force' arrow on a free-body diagram.
Vertical Circle: Top vs Bottom
At the top, T + mg = mv²/r (tension minimum); at the bottom, T − mg = mv²/r (tension maximum). Minimum speed at top of a string-swung circle: √(gr).
Conical Pendulum
T cosθ = mg and T sinθ = mv²/r. Combining gives v² = gr tanθ; the period depends on the vertical height of the cone, not the string length directly.
Flat Curve Maximum Speed
Static friction supplies the centripetal force: μ_s mg = mv²/r, so v_max = √(μ_s g r), independent of the car's mass.
Frictionless Banked Curve
tanθ = v²/(gr). Below the design speed the car tends to slide down the bank; above it, up the bank. Friction extends the safe range of speeds.
Non-Uniform Circular Motion
If speed changes, there is a tangential component of acceleration in addition to the centripetal component. Total acceleration is the vector sum; net force is not purely radial.
Gravitational Field Strength Inside/Outside
Outside a uniform sphere g = GM/r². Doubling the distance from center cuts g to one-fourth. On a planet's surface, g depends on M/R², so a denser, smaller planet can have higher g.
Orbital Speed and Radius
v = √(GM/r): closer orbits are faster. Orbital speed is independent of the satellite's mass, so a bolt and a space station in the same orbit move identically.
T² ∝ r³ for orbits around the same central body; T² = 4π²r³/(GM). Doubling the orbital radius multiplies the period by 2^1.5 ≈ 2.8.
Apparent Weightlessness in Orbit
Astronauts float because they and the station are both in free fall with the same acceleration; gravity at ISS altitude is still about 90 % of surface value.
Geostationary Orbit
An equatorial orbit with period 24 h so the satellite stays above one point; the radius follows from Kepler's law and is about 42,000 km from Earth's center.
Gravitational vs Inertial Mass
Gravitational mass determines the force of gravity on an object; inertial mass determines its resistance to acceleration. Their equality is why all objects fall with the same g.
Effect of Earth's Rotation on Weight
At the equator part of gravity provides centripetal acceleration (about 0.03 m/s²), so a scale reads slightly less there than at the poles.
Elliptical Orbits (qualitative)
Speed is greatest at closest approach (perihelion) and least at farthest (aphelion), consistent with energy conservation; angular momentum is conserved because gravity exerts no torque.