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5.11. Physics I (Mandatory)

5.11.1. Justification ↑ Back to top

Physics I introduces the foundations of classical mechanics as a mathematical and experimental discipline. Through the study of kinematics, Newtonian dynamics, conservation principles, and rotational motion, students acquire the analytical tools needed to model and solve problems of the physical world. This course provides the indispensable foundation for the study of oscillatory, wave, and electromagnetic phenomena addressed in subsequent courses.

5.11.2. Generales Goals ↑ Back to top

1. Describe the motion of particles in different coordinate systems and formulate the equations of motion from Newton's laws.
2. Apply the principles of work, potential energy, and conservation of mechanical energy to systems with conservative and non-conservative forces.
3. Solve particle-system dynamics problems using conservation of linear momentum and collision analysis.
4. Analyze rotational motion and angular momentum dynamics in systems of particles and extended bodies.

5.11.3. Contribution to Outcomes ↑ Back to top

AG-C07) Computing Knowledge: Applies knowledge of mathematics, science, and computing. (Familiarity)

5.11.4. Content ↑ Back to top

5.11.4.1. Kinematics and Dynamics of Particles (18 hours) [Skills AG-C07] ↑ Back to top

Bibliography: (Serway and Jewett, 2018; Young and Freedman, 2015)

Topics

1. Vector description of position, velocity, and acceleration; Newton's three laws and inertial reference frames
2. Formulation and analytical solution of equations of motion for constant and variable forces
3. Phase space diagrams (position vs. velocity) for visualizing mechanical state, stability, and periodicity
4. Numerical integration of equations of motion using Euler, Verlet, and Runge-Kutta methods
5. Constrained motion and holonomic constraints relevant to robotic linkages and articulated bodies

Learning Outcomes

1. Identify all forces acting on a particle in a given mechanical scenario and draw a correct free-body diagram [Familiarity]
2. Implement a numerical integration algorithm such as the Runge-Kutta method to compute the trajectory of a particle under variable forces [Usage]
3. Construct and interpret phase space diagrams to characterize the stability and periodicity of a simulated mechanical system [Assessment]

5.11.4.2. Work, Energy, and Conservation Laws (16 hours) [Skills AG-C07] ↑ Back to top

Bibliography: (Serway and Jewett, 2018; Tipler and Mosca, 2007)

Topics

1. Work-energy theorem relating net work done to change in kinetic energy
2. Potential energy functions and the force-gradient relation for conservative force fields
3. Conservation of total mechanical energy and conditions for its applicability
4. Energy diagrams for identifying equilibrium points, turning points, and stability
5. Elastic and inelastic collision models: momentum and energy exchange in physics engine implementations

Learning Outcomes

1. Explain the distinction between conservative and non-conservative forces and the conditions under which mechanical energy is conserved [Familiarity]
2. Apply energy conservation methods to compute speeds and positions in one-dimensional motion problems common in physics engine implementations [Usage]
3. Analyze elastic and inelastic collision events, computing post-collision velocities and quantifying energy dissipation [Assessment]

5.11.4.3. Systems of Particles and Linear Momentum (14 hours) [Skills AG-C07] ↑ Back to top

Bibliography: (Young and Freedman, 2015; Tipler and Mosca, 2007)

Topics

1. Definition of center of mass: \(\vec{R}_{CM} = \frac{1}{M}\sum m_i \vec{r}_i\)
2. Linear momentum of a particle and system: \(\vec{p} = m\vec{v}\) and \(\vec{P} = M\vec{V}_{CM}\)
3. Newton's second law for systems: \(\vec{F}_{ext} = \frac{d\vec{P}}{dt}\)
4. Conservation of linear momentum for isolated systems
5. Distinction between internal and external forces in a system
6. Two-body collisions including elastic, inelastic, and completely inelastic cases
7. Coefficient of restitution and its physical meaning in collisions
8. Systems with variable mass such as the rocket equation: \(M\frac{dV}{dt} = v_{ex}\frac{dM}{dt}\)
9. Many-particle systems and their center of mass dynamics
10. Continuous mass distributions and their center of mass calculation using integration

Learning Outcomes

1. Locate the center of mass for a discrete set of particles in One, Two, and Three dimensions [Usage]
2. Determine the total linear momentum of a system from the motion of its center of mass [Usage]
3. Apply conservation of linear momentum to solve collision problems in One and Two dimensions [Usage]
4. Classify collisions as elastic, inelastic, or completely inelastic based on kinetic energy conservation [Familiarity]
5. Calculate the coefficient of restitution from pre-collision and post-collision velocities [Usage]
6. Solve the rocket equation to determine velocity as a function of ejected mass [Usage]
7. Analyze how internal forces affect individual particles but not the total momentum of a system [Assessment]
8. Integrate to find the center of mass of symmetric continuous bodies such as rods, disks, and spheres [Usage]

5.11.4.4. Rotational Motion and Angular Momentum (16 hours) [Skills AG-C07] ↑ Back to top

Bibliography: (Serway and Jewett, 2018; Kleppner and Kolenkow, 2013)

Topics

1. Rotational kinematics including angular displacement, velocity, and acceleration (\(\theta, \omega, \alpha\))
2. Torque definition: \(\vec{\tau} = \vec{r} \times \vec{F}\) and its magnitude calculation
3. Angular momentum of a particle: \(\vec{L} = \vec{r} \times \vec{p}\)
4. Rotational form of Newton's second law: \(\vec{\tau}_{net} = \frac{d\vec{L}}{dt}\)
5. Moment of inertia \(I = \sum m_i r_i^2\) and the parallel axis theorem
6. Rotational kinetic energy: \(K_{rot} = \frac{1}{2}I\omega^2\)
7. Conservation of angular momentum for isolated systems
8. Gyroscopic motion and the phenomenon of precession
9. Rolling without slipping dynamics: \(v_{CM} = R\omega\)
10. Coriolis effect as a manifestation of rotational dynamics in non-inertial frames

Learning Outcomes

1. Relate linear and angular kinematic quantities for circular motion [Usage]
2. Calculate torque about a given axis for a force applied at a specific point [Usage]
3. Determine the moment of inertia for simple geometries such as a rod, hoop, disk, or sphere [Usage]
4. Apply conservation of angular momentum to analyze changes in rotational speed when the moment of inertia changes [Assessment]
5. Compute rotational kinetic energy for a rotating rigid body [Usage]
6. Analyze the motion of objects rolling without slipping down an incline [Assessment]
7. Predict the direction of precession for a spinning top or gyroscope [Assessment]
8. Explain the Coriolis effect in terms of rotating reference frames and its effect on projectiles [Familiarity]

5.11.5. Bibliography ↑ Back to top

Serway, R. A. and Jewett, J. W. (2018). Physics for Scientists and Engineers with Modern Physics. Cengage Learning, 10th edition.

Young, H. D. and Freedman, R. A. (2015). Sears and Zemansky's University Physics with Modern Physics. Pearson Education, 14th edition.

Tipler, P. A. and Mosca, G. (2007). Physics for Scientists and Engineers. W. H. Freeman and Company, 6th edition.

Kleppner, D. and Kolenkow, R. J. (2013). An Introduction to Mechanics. Cambridge University Press, 2nd edition.