Advanced Applications in Mechanics

Formulate and solve kinematic problems where acceleration is a function of time, position, or velocity.

Calculate the work done by non-conservative and path-dependent vector force fields using line integrals.

Derive and solve the differential equation of motion for variable mass systems (e.g., rocket propulsion, falling chains).

Calculate the moment of inertia for complex continuous bodies (e.g., cone, hemisphere) using multivariable integration.

Formulate the integral expressions for net force and torque from position-dependent friction on a rigid body.

Solve problems involving rolling with slipping, including finding the time to transition to pure rolling.

Solve impulse-momentum problems for rigid bodies subjected to eccentric impacts.