EMch 212 Dynamics

(3 credits) Motion of a particle; relative motion;
kinetics of translation, rotation, and plane motion;
work-energy; impulse-momentum;

Pre-requisites : EMCH 211 or E MCH 210, MATH 141

Course Objectives : Students will be able to :
• acquire a working knowledge of vector calculus and to apply it to the description of kinetic and kinematic quantities such as forces, moments, position, velocity, and acceleration.
• apply calculus to correctly relate position, velocity, and acceleration to one another.
• create free body diagrams (FBD) of particles and rigid bodies, i.e., to graphically display the relevant system of forces and moments acting on these bodies at a particular and/or at a generic instant during their motion. In general, only motions in 2D will be considered.
• synthesize the information contained in the FBD and MAD to derive the equations of motion for the particular system at hand.
• create the kinetic or mass-acceleration diagram (MAD) of particles and rigid bodies, i.e., to graphically display the acceleration of the center of mass of these bodies. In general, only motions in 2D will be considered.
• apply elementary algebra and calculus to the solution of the equations of motion. Except for a few elementary cases, such as motions with constant acceleration, the solution process in question does not include the solution of initial value problems.
• apply the work-energy principle to relate the energy of a mechanical system to its spatial configuration variables (i.e., position variables). In general, only motions in 2D will be considered.
• apply the impulse-momentum principle to relate the momentum of a mechanical system to the system of forces applied to it.

### Material to be covered, approximate Schedule, and practice Problems

For all recommended problems ( except for the review problems in () ) the problem statements and solutions are available in the library. Inquire for EMCH 212 at the front desk.

LectureTopicTextRecommended Problems
1 Introductory Topics 11.1-11.4 None
2 Kinematics : Rectangular Coordinates 12.1-12.2 12.3 , 12.8 , 12.16, 12.19
3 FMA Method : Rectilinear Motion 12.3-12.5 12.32, 12.40, 12.46, 12.51
4 FMA Method : Superposition of Rectilinear 12.6 12.53, 12.56, 12.60, 12.62
5 Review and in-class Problems   (12.108), (12.112), (12.115), (12.120)
6 Kinematics : Path Coordinates 13.1-13.2 13.2 , 13.9 , 13.13 , 13.17, 13.20
7 Kinematics : Polar/cylindrical Coordinates 13.3 13.26, 13.35, 13.37, 13.41
8 FMA Method: Path Coordinates 13.4 13.51, 13.53, 13.56
9 FMA Method: Polar/cylindrical Coordinates 13.4 13.58, 13.62, 13.64, 13.66
10 Review and in-class Problems   (13.78), (13.81), (13.85), (13.86)
12 Work of a Force 14.1-14.2 14.2, 14.6, 14.7
13 Principle of Work and Kinetic Energy 14.3 14.11, 14.18, 14.22, 14.24
14 Conservation of Mechanical Energy 14.4 14.28, 14.33, 14.40, 14.45
15 Power and Efficiency 14.5 14.51, 14.54, 14.55, 14.60
16 Principle of Impulse and Momentum 14.6 14.64, 14,68, 14.74, 14.76
17 Principle of Angular Impulse and Momentum 14.7 14.82, 14.84, 14.89, 14.92
18 Review and in-class Problems   (14.117), (14.118), (14.120), (14.127)
22 Kinematics of Relative and Constrained Motion 15.1-15.3 15.2, 15.6, 15.11, 15.21, 15.22
23 Equations of Motion of the Mass Center 15.4 15.26, 15.35, 15.38, 15.44
24 Work-Energy, System of Particles 15.5 15.55 , 15.57 , 15.59
25 Impuls-Momentum, System of Particles 15.6-15.7 15.62, 15.70, 15.72, 15.76, 15.80
26 Impulsive Motion 15.8-15.9 15.88, 15.90, 15.91, 15.98
27 Elastic/plastic Impact 15.10 15.104, 15.108, 15.112, 15.114
28 Review and in-class Problems   15.136, 15.140, 15.144, 15.146
30 Kinematics of Rigid Bodies 16.1-16.3 16.2, 16.6, 16.8, 16.14
31-32 Method of Relative Velocity 16.4 16.18, 16.22, 16.32, 16.35
33-34 Method of Relative Acceleration 16.7 16.57, 16.60, 16.70
35 Mass Moment of Inertia, Angular Momentum 17.1-17.2 17.2, 17.4, 17.6, 17.13
37-40 Equations of Plane Motion 17.4-17.5 17.18, 17.26, 17.30, 17.52, 17.58, 17.64
41 Review and in-class Problems   17.93, 17.102, 17.98, 17.100
42 Work-Energy Methods 18.1-18.4 18.2, 18.10, 18.28, 18.44
43 Impulse-Momentum Methods 18.5-18.6 18.58, 18.69, 18.78, 18.81
44 Impact Problems 18.7 18.83, 18.88, 18.93
45 Review and in-class Problems   18.84, 18.86, 18.92, 18.94
Last revised: 09/14/13