14:440:222 Dynamics
Student takeaway note sheet
Lecture 10: Introduction to kinetics using Newtonian
mechanics & Free-body-diagram & Equation of
motion in rectangular coordinates
In today’s lecture, you will learn:
 Newton’s laws & free-body-diagram
 How to write Newton’s second law using rectangular coordinates?
 Conceptual questions and mathematical problems
Rutgers University
Mechanical and Aerospace Engineering Prof. Annalisa Scacchioli, Ph.D.
14:440:222 Dynamics
Student takeaway note sheet
Introduction to kinetics using Newtonian mechanics
 History
 Galileo Galilei (d. 1642) in Italy began the modern development of
the science of mechanics
 In 1687 Isaac Newton (b. 1642), in UK, published “Principia
Mathematica” containing laws of motion and law of universal
gravitation
 Newton’s laws:
 Kinetics: study of how forces relate to the motion
 Newton’s first law:
 a particle at rest or moving in a straight line with a constant
velocity is in equilibrium
 ∑ 𝐹⃗ = 0 (law of inertia)
 Newton’s second law:
 when an imbalanced force (∑ 𝐹⃗ ≠ 0) acts on a particle,
particle experiences an acceleration in the same direction of
the force impressed 𝑎⃗ =
𝐹⃗
𝑚
 ∑ 𝐹⃗ = 𝑚𝑎⃗ (equation of motion)
 Newton’s third law:
 to every action there is an opposed an equal reaction.
 𝐹⃗𝐴𝐵 = −𝐹⃗𝐵𝐴 (action-reaction)
 Newton’s universal gravitation law:
 every pair of particles in the universe exerts on one other a
mutual gravitational force of attraction
𝑚 𝑚
 𝐹𝑔 = 𝐺 12 2
𝑟12
 Solving particle kinetics problems using Newtonian mechanics:
 Type A problem:
 given forces, use kinetics to find acceleration and then use
kinematics to find velocity, space, and time
 Type B problem:
 given velocity, space, and time, use kinematics to find
acceleration and then use kinetics to find forces
Rutgers University
Mechanical and Aerospace Engineering Prof. Annalisa Scacchioli, Ph.D.
14:440:222 Dynamics
Student takeaway note sheet
Modeling elastic force and tension
 Friction force 𝐹𝑓 :
 We use a linear model to describe the friction force Ff = μN, where
𝜇 is the friction coefficient and 𝑁 is the normal force
 Spring force 𝐹𝑠 :
 It is opposite to the force that produced the deformation
 𝐹𝑠 = 𝑘∆𝑥 = 𝑘(𝑥 − 𝑥0 )
 Tension T:
 It is the force transmitted by a rope when forces are applied to it
 It acts in the direction along the medium and it is constant
 If strings and pulleys are massless the tension 𝑇 is the same on
either side of the pulley
Solving problems using FBD and rectangular coordinates
1. Draw a picture indicating all key features in the problem identifying
givens and unknowns
2. For each object draw the free-body-diagram (FBD):
 Draw all the forces acting on it: do not include any internal forces
or forces exerted by the body on some other body!
 Select a coordinate system and show it in the FBD
 when the direction of the acceleration is known in
advance, chose that direction as +x-axis
 can choose different reference frames for each body-all
must be must be inertial!
 Determine components of the forces with reference to these axes
3. If there are geometrical relationship between two or more bodies, relate
them algebraically
4. Write down Newton’s equation of motion for each body and solve for
unknowns: 𝐹⃗ = 𝑚𝑎⃗
 Equations of motion in rectangular coordinates:
 ∑ 𝐹𝑥 = 𝑚 𝑎𝑥
 ∑ 𝐹𝑦 = 𝑚 𝑎𝑦
Rutgers University
Mechanical and Aerospace Engineering Prof. Annalisa Scacchioli, Ph.D.
14:440:222 Dynamics
Student takeaway note sheet
FBD dos and don’ts: orienting the body
FBD does and don’ts: orienting the coordinate system
FBD dos and don’ts: redundant forces
Rutgers University
Mechanical and Aerospace Engineering Prof. Annalisa Scacchioli, Ph.D.