Mistake Master

Circular Motion

Move in a circle at constant speed and you are still accelerating: the velocity vector keeps rotating, and a rotating velocity is a changing velocity. The acceleration that bends the path always points toward the center of the circle, with magnitude $a_c = \dfrac{v^2}{r}$. Whatever real force happens to point toward the center (tension in a string, friction on a turning car, gravity on an orbiting satellite) plays the role of the centripetal force. There is no separate "centripetal" entry on the free-body diagram.

center r v ac ac points inward always perpendicular to v ac = v2 / r double v → quadruple ac CCW around the track
A ball moving counterclockwise on a circular track at constant speed. The blue velocity arrow points along the path, perpendicular to the radius. The pink centripetal acceleration arrow points inward, toward the center, with magnitude $v^2/r$. The acceleration changes the direction of the velocity, not its size.
Hold the Circle · Open the sandbox →

Two pitfalls. The outward push students feel on a turn is real but it is on the seat or the wall, not on them; the wall pushes them inward, and they feel the equal-and-opposite reaction. And students draw a centripetal force alongside tension or normal force, double-counting the inward pull, when "centripetal" is just a role one of the real forces is already playing. The lesson walks both.

The work

3 ways in · any order
Lesson
Circular Motion

Read the lesson. Two worked examples (car on a flat circular curve, minimum speed at the top of a vertical loop) followed by a ten-scenario applet that drills the role-not-a-force distinction, the inward direction of $a_c$, and the $v^2/r$ scaling.

Skill check · 10 scenarios
Diagnostic
10-item topic check

Ten multiple-choice items on centripetal acceleration's direction and magnitude, the role-not-a-force misread, and the $v^2/r$ scaling traps where doubling speed quadruples the required centripetal force.

Not started · 10 items · ~15 min
Targeted Practice
Drill a single misconception

Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the misconception and you move on.

Take the diagnostic to identify your misconceptions