Circular Motion & Gravitation
This page covers the core ideas now; worked examples and practice problems will keep expanding.
1. Centripetal Acceleration & Force
An object moving in a circle at constant speed is still accelerating — its velocity's direction is constantly changing, even though its magnitude (speed) isn't. That acceleration always points toward the center of the circle, which is why it's called centripetal ("center-seeking").
vtangential speed (m/s) — the object's speed along the circular path.rradius (m) — distance from the center of the circular path.accentripetal acceleration (m/s²) — directed toward the center.
"Centripetal force is a separate, real force pushing outward." False — centripetal force is not a new force; it's the name for whatever net inward force happens to be causing the circular motion (tension, gravity, friction, normal force). There's no outward force on the object itself; the sensation of being "thrown outward" is your own inertia resisting the inward turn.
2. Newton's Law of Gravitation
Ggravitational constant ≈ 6.67 × 10⁻¹¹ N·m²/kg².m₁, m₂masses of the two objects (kg).rdistance between the centers of the two masses (m).
Gravity falls off with the square of distance — doubling the distance between two objects cuts the gravitational force to one quarter, not one half.
3. Orbits
An orbit is just circular (or elliptical) motion where gravity itself supplies the centripetal force. Setting gravitational force equal to the required centripetal force lets you solve for orbital speed:
Notice the orbiting object's own mass cancels out entirely — a satellite's mass never affects the speed needed to maintain a given orbital radius.
4. Simulator
5. Practice Problems
1. A 0.5 kg ball on a string moves in a circle of radius 1.2 m at 4 m/s. Find the tension in the string.