Premed · Premed · Physics 1
Lecture 4: Newton's Laws of Motion
Physics I — Mechanics & Thermodynamics
Learning Objectives
By the end of this lecture, students will be able to:
- State and explain Newton's three laws of motion
- Define force, mass, weight, and the concept of inertia
- Identify and classify common forces (gravity, normal, tension, friction)
- Draw and interpret free-body diagrams
- Apply Newton's second law to solve problems involving one or more forces
Lecture Content
I. The Concept of Force
A force is a push or pull exerted on an object by another object or field. Force is a vector quantity with both magnitude and direction, measured in the SI unit of Newtons (N), where 1 N = 1 kg m/s^2. Forces can be classified as contact forces (normal, friction, tension, applied) or non-contact forces (gravity, electromagnetic). When multiple forces act on an object, the net force (or resultant force) is the vector sum of all individual forces: F_net = Sum of F_i.
II. Newton's First Law — The Law of Inertia
Newton's first law states that an object at rest remains at rest, and an object in motion continues in motion with constant velocity, unless acted upon by a net external force. The property that describes an object's tendency to resist changes in its state of motion is called inertia, and mass provides a quantitative measure of inertia. Greater mass means greater inertia.
This law also defines inertial reference frames: frames in which Newton's laws hold true. An inertial frame is one that is not accelerating. The ground (approximately) and a train moving at constant velocity are inertial frames, while a braking car or a spinning merry-go-round are non-inertial frames. A direct consequence of the first law is that if F_net = 0, then a = 0, meaning the object is in equilibrium.
III. Newton's Second Law — F = ma
Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass: F_net = ma. This is a vector equation that holds for each component independently, giving F_net,x = m a_x and F_net,y = m a_y. The second law encompasses the first law as the special case where F_net = 0.
Mass (m) is an intrinsic, scalar property of the object measured in kilograms. Acceleration is the response to the net force: more force produces more acceleration, while more mass reduces the acceleration for a given force. It is crucial to remember that F_net is the vector sum of ALL forces acting on the object, not just a single force.
IV. Newton's Third Law — Action and Reaction
Newton's third law states that for every action, there is an equal and opposite reaction. If object A exerts a force on object B, then object B exerts a force on object A that is equal in magnitude and opposite in direction: F_{A on B} = -F_{B on A}. Third-law pairs always act on different objects, are always the same type of force (both gravitational, both normal, etc.), and exist simultaneously.
A common misconception is that third-law pairs cancel each other out. They do not, because they act on different objects. Forces cancel only when they act on the same object.
<image>Panel A: A book resting on a table. Forces on the book: weight W downward (Earth pulls book) and normal force N upward (table pushes book). These are NOT a third-law pair — they are different types of force on the same object. Panel B: Third-law pairs identified: (1) Earth pulls book down / book pulls Earth up (gravitational pair), (2) table pushes book up / book pushes table down (normal force pair). Arrows are color-coded to distinguish pairs acting on different objects.</image>
V. Weight and Mass
Mass (m) is a measure of the amount of matter and inertia in an object. It is a scalar quantity that is independent of location. Weight (W), on the other hand, is the gravitational force acting on an object: W = mg, directed toward the center of the Earth. At Earth's surface, g = 9.80 m/s^2, but weight varies with location because g differs on the Moon, in orbit, and at different altitudes. An object's mass remains the same everywhere, but its weight changes with the local value of g.
Apparent weight is the normal force a person actually feels, which is what a bathroom scale reads. In an accelerating elevator, apparent weight differs from true weight. When the elevator accelerates upward, apparent weight exceeds mg, making the person feel heavier. When it accelerates downward, apparent weight is less than mg. In free fall, the apparent weight is zero, producing the sensation of weightlessness.
VI. Free-Body Diagrams (FBDs)
A free-body diagram isolates a single object and shows all forces acting on it as arrows. The procedure for drawing an FBD involves identifying the object of interest, representing it as a dot or simple shape, identifying all forces acting on the object (not forces the object exerts on others), drawing each force as an arrow starting from the object and pointing in the correct direction, labeling each force (W, N, T, f, F_applied, etc.), and choosing a coordinate system aligned with the expected acceleration if possible.
When constructing an FBD, there are several common forces to check for: weight (always present near a massive body), normal force (present when the object contacts a surface), tension (present when attached to a string, rope, or cable), friction (present when surfaces are in contact and there is relative motion or a tendency to slide), and any applied or push/pull forces.
<image>A step-by-step illustration of constructing a free-body diagram. Step 1: A block on a ramp is shown in context. Step 2: The block is isolated as a dot. Step 3: Weight vector drawn downward. Step 4: Normal force drawn perpendicular to the ramp surface. Step 5: Friction force drawn parallel to the ramp surface (up the incline). Step 6: A tilted coordinate system is chosen with x-axis along the ramp and y-axis perpendicular to it. Components of the weight vector along these axes are shown as dashed lines.</image>
VII. Applying Newton's Second Law
The general problem-solving framework for Newton's second law begins with drawing a clear sketch, identifying all objects of interest, and drawing a free-body diagram for each. Choose a convenient coordinate system for each object and write Newton's second law in component form: Sum F_x = ma_x and Sum F_y = ma_y. If needed, identify constraints such as objects connected by a rope sharing the same magnitude of acceleration, then solve the resulting system of equations.
For objects in equilibrium (a = 0), the conditions simplify to Sum F_x = 0 and Sum F_y = 0. For objects on inclined planes, it is advantageous to tilt the coordinate system so one axis runs parallel to the surface. In this tilted frame, the weight component along the incline is mg sin(theta) and the component perpendicular to it is mg cos(theta).
<image>A system of two blocks connected by a string over a frictionless pulley (Atwood machine). Block m1 hangs on the left, block m2 hangs on the right (m2 > m1). Free-body diagrams are drawn for each block separately, showing weight downward and tension upward for each. Newton's second law equations are written beside each FBD, with a note that the string constraint means both blocks share the same magnitude of acceleration a and the same tension T.</image>
