Unit 03 · Circular Motion & Gravitation
Motion in a circle is accelerated motion, even at constant speed — because direction is changing. This unit builds the idea of centripetal acceleration pointing toward the center, identifies what real force supplies it in each case, and then scales the same reasoning up to Newton's law of universal gravitation and the orbits it explains. Mastery means you never write "centrifugal force" as a cause, and you can connect a satellite's speed, radius, and period from first principles.
| Criterion | Not yet | Approaching | Mastered |
|---|---|---|---|
| Centripetal acceleration & force | Thinks an object in a circle has no acceleration at constant speed. | Knows there is acceleration but points it the wrong way. | Shows centripetal acceleration points to the center, uses v²/r, and explains why speed can be constant while velocity changes. |
| Source of the centripetal force | Invents a "centrifugal force" pushing outward. | Names a real force but not consistently across situations. | Identifies the actual force supplying the centripetal requirement — tension, friction, gravity, or normal — in each case. |
| Universal gravitation | Confuses mass with weight; ignores distance. | Uses the gravitation equation but mishandles the inverse-square. | Applies the inverse-square law correctly and distinguishes mass from weight in any gravitational field. |
| Orbits & satellites | Treats orbit as unrelated to gravity. | Links gravity to orbit but cannot relate speed, radius, and period. | Derives the relationship among orbital speed, radius, and period and explains why an orbit is continuous free fall. |
| Lab technique (centripetal apparatus) | Swings the mass erratically; takes no repeatable data. | Collects data but does not control the radius or period cleanly. | Uses a conical pendulum or centripetal-force apparatus to measure force versus speed and compares to v²/r with uncertainty. |
| Integration (cross-domain) | Treats the science as isolated facts; makes no cross-domain connection. | Names a link to history, reading, or writing but cannot defend why it matters. | Connects the unit to its anchor across History · Reading · Writing (plus chosen electives) and defends why the connection matters. |
“Nothing pushes the ball outward — the string tension pulls it inward, and that’s the centripetal force. If the string snaps, it flies off along a tangent, not outward. A satellite is the same idea: gravity is the inward pull, and the orbit is just free fall that keeps missing the ground.”
“Centrifugal force throws it outward, and gravity is stronger up high because you’re closer to space.”
You demonstrate this unit through centripetal-force labs plus short oral checks where you reason about what supplies the inward force aloud — not a multiple-choice test. A criterion counts as mastered only when you can both take clean data and justify the physics behind it. Mastery is demonstrated, not awarded.
A 5-page clipboard packet — unit overview, key terms, the mastery rubric, anchor examples, and a score sheet you can print and grade against.