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Review Material for Dynamics Portion of the Fundamentals of Engineering Exam

Chuck Krousgrill Professor, School of Mechanical Engineering

This packet contains review material on the area of dynamics in the topics listed below. Solution videos for a extensive set of examples related to these topics can be found on the course blog for ME 274: https://www.purdue.edu/dynamics . To view these videos, click on the “Lecture Example Videos” link on the right side of the blog page. To help you locate the appropriate solution videos, the chapter and section numbers for the videos are provided in square brackets below. Topics

1. Particle kinematics [section 1A]

2. Rigid body kinematics [sections 2A-2C]

3. Kinetics equations for particles and rigid bodies

- Newton’s 2nd law for particles [section 4A]

- Newton-Euler equations for rigid bodies [section 5A]

- Work-energy equation for particles [section 4B]

- Work-energy equation for rigid bodies [section 5B]

- Linear impulse-momentum equations for particles [section 4C]

4. Vibrations [sections 6A-6C]

FE Exam review material cmk 2

1. PARTICLE KINEMATICS

Cartesian description

Lecture Material

As always, the velocity and acceleration of point P are given by the first and second time derivatives,respectively, of the position vector ~r for P:

~v =d~r

dt

~a =d2~r

dt2

The kinematic equations for the Cartesian, path and polar descriptions are derived in the followingnotes. The following figures showing the kinematic variables and unit vectors will be used in thesederivations.

Cartesian, path and polar kinematics I-4 ME274

Lecture Material As always, the velocity and acceleration of point P are given by the first and second time derivatives, respectively, of the position vector r for P:

v = drdt

a = d2 r

dt2

The kinematic equations for the Cartesian, path and polar descriptions are derived in the following notes. The following figures showing the kinematical variables and unit vectors will be used in these derivations. Cartesian kinematics Here we write the position vector for P in terms of its x and y components and corresponding unit vectors: r = x i + y j Therefore, through differentiation with respect to time:

v =drdt

= !x i + !y j

a =d2r

dt2= !!x i + !!y j

x

y P

path of P

Cartesian description

P

path of P

s

C

!

Path description

r

P

path of P

!

O x

y

Polar description

i

j en et er

e!


Path description


Polar description


2. RIGID BODY KINEMATICS


3. KINETICS EQUATIONS FOR PARTICLES AND RIGID BODIES Summary table


Newton’s 2nd law for particles


Newton-Euler equations for rigid bodies


Work-energy equation for particles


Work-energy equation for rigid bodies


Linear impulse-momentum equation for particles


Linear impulse-momentum equation for particles (continued)


4. VIBRATIONS

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