Concept Checklist (with links to videos)

Particle Dynamics

1. Understand the concept of an ‘inertial basis.’ Sect 2.2.2, see also Newtons laws in non-inertial bases
2. Be able to idealize an engineering design as a set of particles, and know when this idealization will give accurate results. Sect 2.1
3. 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
4. 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
5. Be able to analyze straight line motion of particles with constant acceleration Sects 2.2.5, 2.4, Example 2.5
6. Be able to analyze straight line motion of particles with variable acceleration Sect 2.2.5, 2.3 Example 2.6
7. Be able to describe circular motion in Cartesian and normal-tangential coordinates Sect 2.9, 2.11, Examples 2.10, 2.12
8. 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
9.  Be able to describe motion in polar coordinates Sect 2.15, Examples 2.16, 3.3.4
10. Be able to convert between Cartesian to normal-tangential or polar coordinate descriptions of motion Sect 2.8, Examples 2.16, 3.3.5
11. 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
12. 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
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
14. 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
15. 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
16. 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

1. 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
2. Know the definition of kinetic energy of a particle Sect 4.1.2
3. Understand power-work-kinetic energy relations for a particle Sect 4.1.3
4. Be able to use work/power/kinetic energy to solve problems involving particle motion Examples 4.1.7, 4.1.8, 4.1.9
5. Be able to distinguish between conservative non-conservative and workless forces Sect 4.2.1
6. Be able to calculate the potential energy of a conservative force Example 4.2.3
7. Be able to calculate the force associated with a potential energy function Example 4.2.4
8. Know the work-energy relation for a system of particles; (and energy conservation for a closed system) Sect 4.2.6
9. Use energy conservation to analyze motion of conservative systems of particles Examples 4.2.7, 4.2.8, 4.2.9, 4.4.5
10. Know the definition of the linear impulse of a force Sect 4.3.1
11. Know the definition of linear momentum of a particle Sect 4.3.1
12. Understand the impulse-momentum (and force-momentum) relations for a particle Sect 4.3.2, Examples 4.3.3, 4.3.4
13. Understand impulse-momentum relations for a system of particles (momentum conservation for a closed system) Sect 4.4.1, Sect 4.4.2
14. 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
15. Know the definition of restitution coefficient for a collision Sect 4.5.1
16. 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
17. Know the definition of angular impulse of a force Sect 4.6.1
18. Know the definition of angular momentum of a particle Sect 4.6.1
19. Understand the angular impulse-momentum relation for a particle Sect 4.6.2
20. Be able to use angular momentum to solve central force problems/impact problems Examples 4.6.3, 4.6.4

Vibrations

1. Understand simple harmonic motion (amplitude, period, frequency, phase) Sect 5.2, Example 5.3
2. Understand the motion of a vibrating spring-mass system (and how the motion is predicted) Sect 5.4.1
3. 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,
4. Understand the concept of natural frequencies and mode shapes for vibration of a general undamped  linear system Sect 5.4.2
5. Be able to identify the number of degrees of freedom and vibration modes in an idealization of a system Sect 5.4.3
6. Combine series and parallel springs to simplify a system Sect 5.4.7
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
8. 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,
9. Understand natural frequency, damped natural frequency, and ‘Damping factor’ for a dissipative 1DOF vibrating system Sect 5.5.2, Sect 5.5.3
10. 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
11. Understand underdamped, critically damped, and overdamped motion of a damped 1DOF vibrating system Sect 5.5.2
12. Be able to determine damping factor from a measured free vibration response Sect 5.5.7 Examples 5.6.4
13. Be able to predict motion of a freely vibrating 1DOF system given its initial velocity and position.  Example 5.5.6
14. 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
15. Understand (qualitatively) meaning of ‘transient’ and ‘steady-state’ response of a forced vibration system. Sect 5.6.1
16. 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,
17. 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
18. 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
19. Use forced vibration concepts to design engineering systems Examples 5.6.9, 5.6.13
20. Determine natural frequency and damping from a forced vibration response (eg swept sin test) Sect 5.6.5

Rigid Bodies

1. Understand and manipulate rotation matrices (tensors) in 2D and 3D Sect 6.1.1, 6.1.3, Examples 6.1.2, 6.1.4
2. 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
3. Understand formulas relating velocity/acceleration of two points on a rigid body Sect 6.1.9, Example 6.1.10
4. Understand constraints at joints and contacts between rigid bodies Sect 6.2, Examples 6.2.1, 6.2.2
5. 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
6. Be able to analyze motion in systems of gears Sect 6.3.1, 6.3.4, Examples 6.3.2, 6.3.5
7. 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
8. 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
9. Be able to calculate the center of mass and mass moments of inertia of simple shapes; Examples 6.4.5, 6.4.10
10. Understand the physical significance of the inertia matrix Sect 6.4.8
11. 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
12. Understand the meaning of a ‘force couple’ or ‘pure moment/torque’ Sect 6.5.1
13. Understand the 2D force-linear momentum and moment-angular momentum formulas:

14. Understand the special case of these equations for fixed axis rotation Sect 6.5.8, Examples 6.5.9, 6.5.10
15. 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
16. 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
17. 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