5: Newton's Laws of Motion
- Page ID
- 104129
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)This chapter introduces two new models for understanding motion and interactions: the Galilean Space-Time Model and the Force Model. We begin by defining vectors, essential for representing physical quantities like velocity, force, and displacement that have both magnitude and direction. Using vectors, we analyze how objects move and interact in space and time. Newton's Laws of Motion form the basis of the Force Model, with each law clarifying how forces govern the dynamics of objects. We discuss various force types, including contact forces (like friction and tension) and long-range forces (such as gravity). Free-body diagrams are introduced as tools for visualizing forces on an object, allowing us to calculate net force and predict motion. Throughout the chapter, examples demonstrate how the Force Model helps explain why objects remain stationary or move, and we set the stage for further exploration of momentum conservation and motion prediction in subsequent chapters.
- 5.1: Overview
- This chapter introduces vectors as essential tools for describing physical quantities, particularly forces. Vectors help explain object dynamics and are foundational for understanding Newton's Laws, which clarify why objects move or stay still. This material serves as a reference for applying vectors and forces in upcoming chapters.
- 5.2: Overview of Vectors
- We introduce vectors, describing both magnitude and direction, essential for analyzing motion and forces. Vectors like velocity and acceleration provide detailed spatial information beyond simple magnitudes. Represented as arrows with direction and length, vectors add and subtract geometrically, with components for each dimension. Understanding vector operations allows precise descriptions of position, displacement, and forces, laying a foundation for Newton’s Laws in later chapters.
- 5.3: The Force model
- We introduce the Force Model, describing forces as vectors that cause changes in an object's motion. Forces act through contact (e.g., friction, tension) or at a distance (e.g., gravity). Newton’s Laws provide structure: the First Law explains balanced forces and inertia, while the Second Law relates force to mass and acceleration. The Third Law states forces between two objects are equal and opposite. This framework is key for analyzing motion in various physical contexts.
- 5.4: Applying the Force Model
- We apply the Force Model using free-body diagrams (FBDs) to analyze forces acting on an object. FBDs represent each force as an arrow, helping to visualize interactions and determine net force. Key examples include tension, normal, frictional, and gravitational forces. By summing forces in each direction, we can predict an object's motion according to Newton's Laws. FBDs simplify problem-solving for scenarios like stationary objects, objects in motion, and systems with balanced or unbalanced for
- 5.5: Wrap-up
- This chapter introduced vectors and Newton's Laws, essential for analyzing forces and predicting motion. We explored calculating net force to determine if a system’s velocity changes. Upcoming chapters will apply these principles to momentum conservation and motion under acceleration, deepening our understanding of dynamics.