circular motion
Summary
Circular motion is motion along a circular path. Even at constant speed the velocity direction keeps changing, so there is a centripetal acceleration a = v²/r toward the center. Most testable: centripetal force is not a new force. It is the net inward force from real forces such as tension, gravity or friction.
Detail
Meaning: An object moves along a circle of radius r. Even at constant speed its velocity vector changes direction, so it accelerates. In uniform circular motion the acceleration points toward the center, and so does the net force. That inward net force comes from real interactions such as tension, gravity, friction, the normal force or a magnetic force. If it disappears, the object leaves along a straight line tangent to the circle, not radially outward.
Equation: Fc = mv²/r = mω²r, where Fc is the centripetal force (N), m is mass (kg), v is speed (m/s), ω is angular speed (rad/s) and r is radius (m). Also v = ωr = 2πr/T, where T is the period (s).
On the MCAT: Identify which force plays the centripetal role: friction for a car on a flat curve, gravity for an orbit (GMm/r² = mv²/r), tension for a ball on a string, the magnetic force for a charge (qvB = mv²/r). Predict changes: doubling v quadruples the required force, and halving r doubles it. Because the centripetal force is perpendicular to the velocity, it does no work and the speed stays constant.
Common confusion: Centrifugal force is not a real force acting on the object in an inertial frame. It is the apparent outward push felt in a rotating frame, caused by inertia. Also, constant speed does not mean zero acceleration, because velocity is a vector.
Sources
- Physics (Giancoli)
- Fundamentals of Physics (Halliday, Resnick, Walker)
- College Physics (Serway, Vuille)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.