In this video, David quickly explains each torque and angular concept and does a sample question for each one. Created by David SantoPietro.

Diagnostic studies and discussion of their implications for the theory of the structure and general circulation of the Earth's atmosphere. Includes some discussion of the validation and use of general circulation models as atmospheric analogs.

Fundamental concepts of quantum mechanics: wave properties, uncertainty principles, Schrodinger equation, and operator and matrix methods. Basic applications to: one-dimensional potentials (harmonic oscillator), three-dimensional centrosymetric potentials (hydrogen atom), and angular momentum and spin. Approximation methods: WKB method, variational principle, and perturbation theory.

Join the ladybug in an exploration of rotational motion. Rotate the merry-go-round to change its angle, or choose a constant angular velocity or angular acceleration. Explore how circular motion relates to the bug's x,y position, velocity, and acceleration using vectors or graphs.

Second subject of two-term sequence on modeling, analysis and control of dynamic systems. Kinematics and dynamics of mechanical systems including rigid bodies in plane motion. Linear and angular momentum principles. Impact and collision problems. Linearization about equilibrium. Free and forced vibrations. Sensors and actuators. Control of mechanical systems. Integral and derivative action, lead and lag compensators. Root-locus design methods. Frequency-domain design methods. Applications to case-studies of multi-domain systems.

Together, this course and 8.06 Quantum Physics III cover quantum physics with applications drawn from modern physics. Topics covered in this course include the general formalism of quantum mechanics, harmonic oscillator, quantum mechanics in three-dimensions, angular momentum, spin, and addition of angular momentum.

A two-semester subject on quantum theory, stressing principles: uncertainty relation, observables, eigenstates, eigenvalues, probabilities of the results of measurement, transformation theory, equations of motion, and constants of motion. Symmetry in quantum mechanics, representations of symmetry groups. Variational and perturbation approximations. Systems of identical particles and applications. Time-dependent perturbation theory. Scattering theory: phase shifts, Born approximation. The quantum theory of radiation. Second quantization and many-body theory. Relativistic quantum mechanics of one electron. This is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

" The goal of this course is to illustrate the spectroscopy of small molecules in the gas phase: quantum mechanical effective Hamiltonian models for rotational, vibrational, and electronic structure; transition selection rules and relative intensities; diagnostic patterns and experimental methods for the assignment of non-textbook spectra; breakdown of the Born-Oppenheimer approximation (spectroscopic perturbations); the stationary phase approximation; nondegenerate and quasidegenerate perturbation theory (van Vleck transformation); qualitative molecular orbital theory (Walsh diagrams); the notation of atomic and molecular spectroscopy."

The modules posted below aim to provide digital resources for students and instructors. Providing students on-demand digital, multimedia, open-access resources which can be watched repeatedly at convenient times can serve as one path to improving student success in introductory physics courses The modules have been created for each topic covered in calculus-based introductory physics courses. Each module includes:Videos reviewing the laws and concepts, and videos with step-by-step problem solving providing students with additional aid in learning the material. (i) Review Videos summarize major topics after students had encountered them in class and highlight their application to common and significant problems. This resource incorporates explanations, derivations, and demonstrations to illustrate a concept; (ii) Problem-Solving Videos present detailed solutions to multi-step questions which students might encounter when working through textbook problems or on major summative assessments. This in-depth approach was structured to guide students in improving their problem-solving skills and techniques, as well as address common mistakes. More than one hundred videos have been created for different types of learners. This is a resource for both students and instructors.Textbook-independent homework problem sets that could be implemented via LMS. The homework has a mix of multiple-choice and free-response problems aiming to develop student critical thinking. Detailed solutions to all problems are provided so that the students can compare their results with the solution, or an instructor can understand what was intended for the solution if modification of the problem is desired. This is a resource for both instructors and students. Video demonstration experiments for each topic that will allow the instructors around the State of Texas to bring physics experiments to their classrooms (instructor resource). The videos merely show the experiment taking place without any explanation of the underlying physics. This gives the instructor complete freedom to tailor the explanation to their class. A text with a brief description of the experiments is provided. 

A mixture of multiple-choice and free-response problems aimed at developing critical thinking. Detailed solutions to all problems are provided.

Problem-Solving Videos present detailed solutions to multi-step questions. These videos are structured to improve problem-solving skills.

Review Videos summarize major topics. This resource incorporates explanations, derivations, and demonstrations to illustrate a concept.

Investigate how torque causes an object to rotate. Discover the relationships between angular acceleration, moment of inertia, angular momentum and torque.

Investigate how torque causes an object to rotate. Discover the relationships between angular acceleration, moment of inertia, angular momentum and torque.

University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. This textbook emphasizes connections between between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result.