PART 4. PLANAR KINETICS OF RIGID BODIES
Motion and Deformation of Mechanical
Systems with 1 Degree of Freedom (1DOF) – combination translation and
rotational displacements
Textbook Chapter 5 (Lectures 2431)
Acronyms: M:
mass, K: stiffness, C: damping, EOM: equation of motion, SEP: static
equilibrium position, DOF: degree of freedom, FBD: free body diagram, CME:
Principle of Conservation of Mechanical Energy
Lecture (get me) 
Major Topics/WHAT
YOU WILL LEARN 
Recommended homework
problems 
What is a rigid body? Properties of inertias (mass, center of mass and mass moments of
inertia): development of equations. Parallel axis formula and restrictions to
its application. Example: determine mass center and moment of inertia of a physical assembly. Steps in procedure. Use published Tables containing useful mass properties 
Appendix
C.2, C.4, C.6 

Motion of a rigid body on a plane:
derivation of force and moment EOMs in Cartesian coordinates. Vector
analysis. Reduced forms for the moment EOM: about mass center, about fixed
point in inertial space. Applications. 1DOF torsional vibrations: definition
of torsional stiffness, natural frequency, and similitude to response of
1DOF MKC system. Fixed axis rotation: simple rotor on bearings, pulleys
connected by belts, gear transmission 
5.1, 5.3, 5.4, 5.5 

Kinetic energy of rigid body in planar motion
(translation and rotation). Examples of fixed axis rotation: derivation of equations
from CME: rotor on bearings, torsional vibrations, pulleys connected by
belts. Same examples as seen from conservation of
mechanical energy 
Work
5.1, 5.2 (without viscous damping) and derive the EOM using CME. Rework 5.4,
5.5 using CME 

Nonlinear EOMs for compound pendulum
connected to (linear) spring and viscous damper: FBDs,
application of force and moment equations, geometric nonlinearities at linear
element (K, C) connections, linearization of EOM about SEP. EOM derived from
CME. Preload in spring elements. Finding natural frequencies and motions for
bars and plates connected to springs and dampers. 
5.7, 5.9, 5.10 

More compound pendulum
applications: nonlinear spring force –displacement relations and
linearization of EOMS for motions about SEP. Rigid body motion with prescribed acceleration of
pivot support: FBDs,
application of force and moment equations. Equations for reaction forces,
interpretation of results 
5.21, 5.22, 5.24 5.28, 5.30, 5.31 

Motion of cylinders rolling w/o slipping. FBDs,
identification of forces and rolling constraint, derivation of EOM.
Definition of Coulomb (dry friction) forces. When will the cylinder slip and
not roll? EOM derived from CME. EOM for imbalanced cylinder rolling down an
inclined plane, oscillations of a half cylinder on a flat plane: prediction
and measurement of natural frequency. 
5.33,
5.34, 5.36 

More applications of rolling w/o slipping motion: cylinder restrained by spring, cylinder rolling
inside a concave surface: FBDs, identification of
forces and rolling constraint, derivation of EOM, linearization and
identification of natural frequency. EOM derived from CME. Example: pulley
assembly connected to spring element 
5.32, 5.37, 5.38 

Examples of
1DOF mechanical systems combining rotation and translation. Using 
5.41,
5.42, 5.69, 5.70 
Get all: Lectures 2431_{}
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