7 | FRQ | Practice Sessions | AP Physics C: Mechanics

DeeDee Messer, an AP Physics C teacher, introduces a mechanics practice session focusing on a free response question involving rotation. She encourages students to download the question or pause the video to work through the problem. The session starts with a triangular rod problem where students must use integral calculus to find the rod's rotational inertia about its left end, given a non-uniform linear mass density. The correct answer is derived through substitution and integration, resulting in 1/2 ml squared, which is verified against the basic formula for rotational inertia.

The session continues with a problem involving a hoop and three identical rods attached to it. Students are tasked with deriving the total rotational inertia of the system about the hoop's center. The solution involves summing the rotational inertia of the hoop and the three rods, leading to an expression of 5/2 ml squared. The scoring criteria for this part are explained, emphasizing the importance of showing the addition of rotational inertias and maintaining consistency with previous answers.

In the next part, the hoop-rod system, initially at rest, experiences a constant force exerted tangentially, causing it to spin. Students must derive an expression for the final angular speed of the system, using variables m, l, f, delta T, and appropriate physical constants. The solution involves understanding torque and Newton's second law for rotating systems, leading to an equation for omega. The scoring for this section is based on the correct use of equations, relating the lever arm to the rod's length, and the correct substitution of the system's rotational inertia from part B.

The session then addresses a scenario where the hoop-rod system rolls without slipping up a ramp. Students are instructed to draw and label the forces acting on the system, emphasizing the importance of not drawing force components and starting each force arrow from its point of application. The forces include gravitational force, normal force, and frictional force, each with a specific direction justified by their physical origins and the system's motion. Scoring for this part focuses on the correct identification and justification of the forces.

The final part of the session involves deriving an expression for the change in height of the hoop's center as it rolls up a ramp. With the assumption of no kinetic friction and energy conservation, the initial kinetic energy (both translational and rotational) is converted into gravitational potential energy at the end. By substituting definitions for energies and specific values, an expression for height change is obtained. The scoring criteria for this section reward the use of conservation of energy principles, correct substitution of linear speed, and accurate representation of the system's mass.