Syllabus, Lecture Videos and Lecture Notes
Quick Links:
- Course Goals >>
- Workload Expectation >>
- Lecture Videos (with pdf copies of notes and MATLAB codes) >>
- Detailed Syllabus (with links to sections of videos) >>
- Concept Checklist (with links to videos) >>
- Electronic Notes (detailed written text) >>
Concept Checklist (with links to videos)
Particle Dynamics
- Understand the concept of an ‘inertial basis.’ Sect 2.2.2, see also Newtons laws in non-inertial bases
- Be able to idealize an engineering design as a set of particles, and know when this idealization will give accurate results. Sect 2.1
- Describe the motion of a system of particles (eg components in a fixed coordinate system components in a polar coordinate system) Sect 2.2.1 et seq; Sect 2.15; see also Examples 3.3.4, 3.3.5, 3.3.6, 3.3.7
- Be able to differentiate position vectors (with proper use of the chain rule!) to determine velocity and acceleration; and be able to integrate acceleration or velocity to determine position vector. Sect 2.2, 2.3
- Be able to analyze straight line motion of particles with constant acceleration Sects 2.2.5, 2.4, Example 2.5
- Be able to analyze straight line motion of particles with variable acceleration Sect 2.2.5, 2.3 Example 2.6
- Be able to describe circular motion in Cartesian and normal-tangential coordinates Sect 2.9, 2.11, Examples 2.10, 2.12
- Be able to describe motion along an arbitrary planar path in normal-tangential coordinates (eg be able to write down vector components of velocity and acceleration in terms of speed, radius of curvature of path). Sect 2.13, Example 2.14
- Be able to describe motion in polar coordinates Sect 2.15, Examples 2.16, 3.3.4
- Be able to convert between Cartesian to normal-tangential or polar coordinate descriptions of motion Sect 2.8, Examples 2.16, 3.3.5
- Be able to draw a correct free body diagram showing forces acting on system idealized as particles Examples 3.2.1, 3.2.2, 3.2.3, 3.3.6, 5.4.5, 5.6.13
- Be able to write down Newton’s laws of motion in rectangular, normal-tangential, and polar coordinate systems Examples 3.2.1, 3.2.2, 3.3.4, 3.3.5, 3.3.6, 5.4.5, 5.6.13
- Be able to obtain an additional moment balance equation for a rigid body moving without rotation or rotating about a fixed axis at constant rate. Examples 3.2.2, 5.4.5, 5.6.13
- Be able to use Newton’s laws of motion to solve for unknown accelerations or forces in a system of particles Examples 3.2.1, 3.2.2, 3.2.3
- Use Newton’s laws of motion to derive differential equations governing the motion of a system of particles Examples 3.3.1, 3.3.3, 3.3.4, 3.3.5, 3.3.6, 5.4.5, 5.6.13
- Be able to re-write second order differential equations as a pair of first-order differential equations in a form that MATLAB can solve Example 3.3.4
Conservation Laws for Particles
- Know the definitions of power (or rate of work) of a force, and work done by a force Sect 4.1.1, Examples 4.1.4, 4.1.5, 4.1.6
- Know the definition of kinetic energy of a particle Sect 4.1.2
- Understand power-work-kinetic energy relations for a particle Sect 4.1.3
- Be able to use work/power/kinetic energy to solve problems involving particle motion Examples 4.1.7, 4.1.8, 4.1.9
- Be able to distinguish between conservative non-conservative and workless forces Sect 4.2.1
- Be able to calculate the potential energy of a conservative force Example 4.2.3
- Be able to calculate the force associated with a potential energy function Example 4.2.4
- Know the work-energy relation for a system of particles; (and energy conservation for a closed system) Sect 4.2.6
- Use energy conservation to analyze motion of conservative systems of particles Examples 4.2.7, 4.2.8, 4.2.9, 4.4.5
- Know the definition of the linear impulse of a force Sect 4.3.1
- Know the definition of linear momentum of a particle Sect 4.3.1
- Understand the impulse-momentum (and force-momentum) relations for a particle Sect 4.3.2, Examples 4.3.3, 4.3.4
- Understand impulse-momentum relations for a system of particles (momentum conservation for a closed system) Sect 4.4.1, Sect 4.4.2
- Be able to use impulse-momentum to analyze motion of particles and systems of particles Examples 4.4.3, 4.4.4, 4.4.5
- Know the definition of restitution coefficient for a collision Sect 4.5.1
- Predict changes in velocity of two colliding particles using momentum and the restitution formula Sect 4.5.2, 4.5.6, 4.5.7, Examples 4.5.3, 4.5.4, 4.5.5, 4.5.8, 4.5.9, 4.5.10
- Know the definition of angular impulse of a force Sect 4.6.1
- Know the definition of angular momentum of a particle Sect 4.6.1
- Understand the angular impulse-momentum relation for a particle Sect 4.6.2
- Be able to use angular momentum to solve central force problems/impact problems Examples 4.6.3, 4.6.4
Vibrations
- Understand simple harmonic motion (amplitude, period, frequency, phase) Sect 5.2, Example 5.3
- Understand the motion of a vibrating spring-mass system (and how the motion is predicted) Sect 5.4.1
- Calculate natural frequency of a 1 degree of freedom linear system (Derive EOM and use the solutions given on the handout) Sect 5.4.1, Examples 5.4.5, 5.4.6,
- Understand the concept of natural frequencies and mode shapes for vibration of a general undamped linear system Sect 5.4.2
- Be able to identify the number of degrees of freedom and vibration modes in an idealization of a system Sect 5.4.3
- Combine series and parallel springs to simplify a system Sect 5.4.7
- Use energy to derive an equation of motion for a 1 DOF conservative system Sect 5.4.8, Example 5.4.10, 6.6.2
- Analyze small amplitude vibration of a nonlinear system (eg pendulum) by linearizing EOM with Taylor series Sect 5.4.9, Example 5.4.10, 5.4.11,
- Understand natural frequency, damped natural frequency, and ‘Damping factor’ for a dissipative 1DOF vibrating system Sect 5.5.2, Sect 5.5.3
- Know formulas for nat freq, damped nat freq and ‘damping factor’ for spring-mass system in terms of k,m,c Sect 5.5.2, Examples 5.5.4, 5.5.5
- Understand underdamped, critically damped, and overdamped motion of a damped 1DOF vibrating system Sect 5.5.2
- Be able to determine damping factor from a measured free vibration response Sect 5.5.7 Examples 5.6.4
- Be able to predict motion of a freely vibrating 1DOF system given its initial velocity and position. Example 5.5.6
- Be able to derive equations of motion for spring-mass systems subjected to external forcing (several types) and solve EOM by comparing to solution tables Sect 5.6.1, 5.6.7, 5.6.10, Example 5.6.13
- Understand (qualitatively) meaning of ‘transient’ and ‘steady-state’ response of a forced vibration system. Sect 5.6.1
- Understand the meaning of ‘Amplitude,’ Magnification, and ‘phase’ of steady-state response of a forced vibration system Sect 5.6.1, 5.6.7, 5.6.10,
- Understand amplitude-v-frequency formulas (or graphs), resonance, high and low frequency response for 3 systems Sect 5.6.1, 5.6.7, 5.6.10
- Determine the amplitude of steady-state vibration of forced spring-mass systems. Example 5.6.2, 5.6.3, 5.6.8, 5.6.9, 5.6.11, 5.6.12, 5.6.13
- Use forced vibration concepts to design engineering systems Examples 5.6.9, 5.6.13
- Determine natural frequency and damping from a forced vibration response (eg swept sin test) Sect 5.6.5
Rigid Bodies
- Understand and manipulate rotation matrices (tensors) in 2D and 3D Sect 6.1.1, 6.1.3, Examples 6.1.2, 6.1.4
- Understand angular velocity and acceleration vectors; be able to integrate / differentiate angular velocities / accelerations for planar motion. Sect 6.1.5, 6.1.7, Example 6.1.6, 6.1.8
- Understand formulas relating velocity/acceleration of two points on a rigid body Sect 6.1.9, Example 6.1.10
- Understand constraints at joints and contacts between rigid bodies Sect 6.2, Examples 6.2.1, 6.2.2
- Be able to relate velocities, accelerations, or angular velocities/accelerations of two members in a system of links or rigid bodies Sect 6.2, Examples 6.2.1, 6.2.2
- Be able to analyze motion in systems of gears Sect 6.3.1, 6.3.4, Examples 6.3.2, 6.3.5
- Understand formulas relating velocity/angular velocity and acceleration/angular acceleration of a rolling wheel Sect 6.3.6, 6.5.6, Example 6.3.7, 6.5.4, 6.5.7
- Understand how to calculate the angular momentum and kinetic energy of a rigid body or system of particles using the inertia matrix (in 3D) or inertia about an axis perpendicular to a symmetry plane (in 2D) Sects 6.4.1, 6.4.3, 6.4.15, Examples 6.4.2, 6.4.4
- Be able to calculate the center of mass and mass moments of inertia of simple shapes; Examples 6.4.5, 6.4.10
- Understand the physical significance of the inertia matrix Sect 6.4.8
- Use parallel axis theorem to shift axis of inertia or calculate mass moments of inertia for a set of rigid bodies connected together Sect 6.4.12, 6.4.13, Example 6.4.14
- Understand the meaning of a ‘force couple’ or ‘pure moment/torque’ Sect 6.5.1
- Understand the 2D force-linear momentum and moment-angular momentum formulas:
- Understand the special case of these equations for fixed axis rotation Sect 6.5.8, Examples 6.5.9, 6.5.10
- Be able to use dynamics equations and kinematics equations to calculate accelerations / forces in a system of planar rigid bodies subjected to forces Examples 6.5.3, 6.5.4, 6.5.5, 6.5.6, 6.5.7, 6.5.9, 6.5.10
- Understand power/work/potential energy of a rigid body; use energy methods to analyze motion in a system of rigid bodies Sect 6.6, Example 6.6.1, 6.6.2, 6.6.3, 6.7.2, 6.7.3
- Use angular impulse – angular momentum relation to analyze motion of systems rigid bodies Sect 6.7, Examples 6.7.1, 6.7.2, 6.7.3