Axis of rotation

Not a physical object, and often not even a real hinge. It is a line you nominate, and the CED writes it into the definition of nearly everything in Unit 5.

• Arc length. EK 5.2.A.1: for a point at a distance $r$ from a fixed axis of rotation, the linear distance travelled as the system rotates through $\Delta\theta$ is $\Delta s = r\,\Delta\theta$.
• [Torque](/glossary/torque). EK 5.3.A.1: torque results only from the force component perpendicular to the position vector from the axis of rotation to the point of application of the force.
• [Lever arm](/glossary/lever-arm). EK 5.3.A.2: the perpendicular distance from the axis of rotation to the line of action of the exerted force.
• [Rotational inertia](/glossary/rotational-inertia). EK 5.4.A.1 ties it to the mass of the system and the distribution of that mass relative to the axis of rotation.

So a force has no single torque, and a body has no single rotational inertia. Both are answers to a question that includes an axis.

Where rotational inertia is smallest. EK 5.4.B.1: a rigid system's rotational inertia in a given plane is at a minimum when the rotational axis passes through the system's center of mass. Any parallel axis gives more, by the amount the parallel axis theorem adds.

What does not depend on it. EK 5.2.A.3: for a rigid system, all points within that system have the same angular velocity and angular acceleration. Linear speed does depend on the distance from the axis, which is why the rim of a wheel outruns the hub.

Scope. The Topic 5.1 and 5.2 boundary statements both limit descriptions of the direction of rotation to clockwise and counterclockwise with respect to a given axis of rotation, and Topic 5.5 adds that AP Physics 1 does not expect students to simultaneously analyze rotation in multiple planes.