Learning Outcomes

Upon completing this lesson, you will be able to:

• State Newton's Three Laws of Motion and explain their physical meaning.
• Differentiate between mass and weight and their roles in the equation of motion.
• Draw a Free-Body Diagram and a Kinetic Diagram for a particle undergoing acceleration.
• Apply the equation of motion $(\Sigma \vec{F} = m\vec{a})$ to solve for unknown forces or accelerations in 2D.
• Integrate kinetics (the study of forces) with kinematics (the study of motion) to solve dynamic problems.

Topics Covered

• Newton's Laws of Motion
• The Equation of Motion
• Free-Body and Kinetic Diagrams
• Problem-Solving Procedure

I. Newton's Laws of Motion

Kinetics is the study of the relationship between the forces acting on a body and the motion of that body. While kinematics describes motion, kinetics explains the cause of that motion. The entire foundation of kinetics rests on Newton's Three Laws.

• Newton's First Law (Law of Inertia): An object will remain at rest, or continue to move with a constant velocity, unless it is acted upon by a net external force.

  • This law defines the state of equilibrium. If

    $$ \Sigma \vec{F} = 0 $$

    then the acceleration $\vec{a} = 0$. This is the domain of Statics.

• Newton's Second Law (The Law of Acceleration): The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

  • This is the central equation of Dynamics:

    $$ \Sigma \vec{F} = m\vec{a} $$

    It applies when the net force is not zero, causing the body to accelerate.

• Newton's Third Law (The Law of Action-Reaction): For every action, there is an equal and opposite reaction. If object $A$ exerts a force on object $B$, then object $B$ simultaneously exerts a force on object $A$ that is equal in magnitude and opposite in direction.

II. The Equation of Motion

Newton's Second Law gives us the equation of motion. It is a vector relationship, meaning it can be broken down into scalar component equations along a coordinate system (e.g., $x$-$y$ axes).

$$ \Sigma \vec{F} = m\vec{a} $$

In a 2D Cartesian system, this single vector equation yields two scalar equations:

$$ \Sigma F_x = ma_x $$

$$ \Sigma F_y = ma_y $$

These equations state that the sum of all force components in a given direction must equal the particle's mass times its acceleration component in that same direction.

III. Free-Body and Kinetic Diagrams

To successfully apply the equation of motion, it is crucial to visualize all the forces and the resulting acceleration. We do this by drawing two separate diagrams.

• Free-Body Diagram (FBD): This is the same diagram we used in statics. It is a sketch of the particle, isolated from its surroundings, showing all external forces acting on it (e.g., weight, tension, normal forces, applied forces).
• Kinetic Diagram: This diagram shows the result of the forces. It is a sketch of the particle showing the mass times acceleration vector, $m\vec{a}$. The $m\vec{a}$ vector always points in the direction of the particle's acceleration.

The equation of motion, $\Sigma \vec{F} = m\vec{a}$, is the mathematical statement that these two diagrams are equivalent.

IV. Problem-Solving Procedure