AP Physics C: Mechanics - Advanced Concept Mastery

Front

Differentiate path length (s) from displacement magnitude (|Δr|) for a moving particle.

Back

Displacement magnitude |Δr| is the absolute value of the change in the position vector: |Δr| = |r_final - r_initial|. Path length s is the total distance traversed along the curved trajectory. Critically, |Δr| can be zero even if s is large (circular motion), and s is always ≥ |Δr|.

Front

Derive the direction of the Coriolis acceleration vector for a moving body.

Back

The Coriolis acceleration is given by a_coriolis = -2Ω × v. To find the direction, use the right-hand rule for the cross product Ω × v (where Ω is angular velocity), then reverse the direction (multiply by -1). In the Northern Hemisphere (Ω up), this deflects moving objects to the right of their velocity.

Front

Analyze the work-energy theorem in the presence of non-conservative forces.

Back

The work-energy theorem states that W_net = ΔK. This can be expanded to W_conservative + W_non-conservative = ΔK. Since W_conservative = -ΔU, we get W_nc = ΔK + ΔU = ΔE_mech. If W_nc = 0, mechanical energy is conserved; if W_nc < 0, mechanical energy is dissipated (e.g., friction).

Front

Explain why mechanical energy is conserved in a system with static friction.

Back

Static friction does no work because the displacement of the contact point is zero (no relative motion). In a rolling object without slipping, the instantaneous velocity of the contact point is zero. Therefore, W_static = 0, and kinetic energy converts between translational (1/2 mv^2) and rotational (1/2 Iω^2) forms without loss.

Front

Compare and contrast Moment of Inertia (I) and Mass (m) in rotational dynamics.

Back

Mass is the scalar measure of translational inertia (resistance to F=ma). Moment of Inertia (I) is the scalar measure of rotational inertia (resistance to τ = Iα). While mass is an intrinsic property, I depends on the mass distribution relative to the axis of rotation (I = ∫ r^2 dm). A 'hoop' has more I than a 'disk' of equal mass.