2.1 Systems and Center of Mass
In physics, before we can analyze the forces acting in a scenario, we must define our system. A system is a collection of objects that we choose to analyze together as a single entity.
Center of Mass (COM): The unique point where the weighted relative position of the distributed mass sums to zero. For a system, it's the point that moves exactly as if all the system's mass were concentrated there and all external forces were applied directly to it.
Center of Mass Formula (1D)
(Also written as xcm = Σmixi / Σmi)
2.2 Forces and Free-Body Diagrams
A force is a push or pull on an object resulting from its interaction with another object. To correctly apply Newton's Laws, we must visualize these forces using Free-Body Diagrams (FBDs).
Rules for Drawing FBDs on the AP Exam
- Represent the object as a solid dot (or simple box).
- Draw arrows pointing away from the dot to represent forces.
- Make the length of the arrows roughly proportional to the magnitude of the forces.
- NEVER draw components of forces on your official FBD (draw them on a separate scratch diagram if needed).
- Label all forces clearly (e.g., Fg, FN, FT, Ff).
⚠️ Remember: Mass and Acceleration are NOT forces. Never include an "ma" vector or an "inertia" vector on a free-body diagram.
2.3 Newton's Third Law
Newton's Third Law describes the fundamental symmetry of nature: forces always exist in pairs.
Newton's Third Law: For every action force, there is a simultaneous reaction force that is equal in magnitude and opposite in direction.
Thought Experiment: The Bug and the Windshield
A heavy truck traveling at 60 mph hits a tiny bug. Which object experiences a greater magnitude of force?
Answer: They experience the EXACT SAME magnitude of force. The bug undergoes a much larger acceleration because it has a much smaller mass (a = F/m), not because the force on it is larger.
2.4 Newton's First Law
Often called the Law of Inertia, this law tells us what happens when forces are balanced.
Newton's First Law: An object at rest remains at rest, and an object in motion remains in uniform motion (constant velocity) unless acted upon by a net external force.
Inertia
The resistance of any physical object to any change in its velocity. Inertia is purely a property of mass. More mass = more inertia.
Translational Equilibrium
When the net force is zero (ΣF = 0). The object has zero acceleration, meaning it is either stationary OR moving with constant velocity.
2.5 Newton's Second Law
This is arguably the most important mathematical tool in mechanics. It connects kinematics (acceleration) to dynamics (forces).
The acceleration of an object is directly proportional to the net force and inversely proportional to its mass.
🎯 Problem-Solving Strategy: Always split Newton's Second Law into perpendicular axes. Analyze the x-direction (ΣFx = max) completely independent of the y-direction (ΣFy = may).
2.6 Gravitational Force
Gravity is an attractive force between two objects with mass.
| Local Gravity (Weight) | Newton's Law of Universal Gravitation |
|---|---|
| Used when near the surface of a planet. | Used when analyzing orbits, or objects very far apart. |
|
Fg = mg
|
Fg = G
m1m2
r2
|
| g = 9.8 m/s2 on Earth (Use 10 m/s2 on the AP Exam to save time!) | G = 6.67 × 10-11 N·m2/kg2 r = distance between centers of mass. |
2.7 Kinetic and Static Friction
Friction is a contact force that opposes sliding motion between surfaces.
Static Friction (Ffs)
Prevents surfaces from sliding. It is a "smart" force—it matches the applied force up to a maximum breaking point.
Kinetic Friction (Ffk)
Occurs when surfaces are actively sliding against each other. It is generally constant.
2.8 Spring Forces
Springs exert a restoring force that pushes or pulls objects back toward an equilibrium position. This relationship is modeled by Hooke's Law.
- Fs = Force applied by the spring
- k = Spring constant (stiffness in N/m)
- Δx = Displacement from equilibrium
- Negative sign (-) indicates the force is a restoring force (points opposite to displacement).
2.9 Circular Motion
When an object moves in a circle at a constant speed, its velocity vector is constantly changing direction. Therefore, it is accelerating, and there must be a net force pointing toward the center of the circle.
Centripetal Acceleration (ac): The acceleration directed radially inward toward the center of the circular path.
⚠️ Centripetal Force is NOT a new force!
"Centripetal" just means "center-seeking". Centripetal force (ΣFc) is simply the Net Force in the radial direction. It must be provided by a real force like tension, gravity, normal force, or friction.
Unit 2 Key Takeaways
A system's center of mass accelerates only if a net external force is applied.
Never draw components or "ma" vectors on an official Free-Body Diagram.
Newton's 3rd Law pairs act on opposite objects and never cancel each other out.
Break ΣF = ma into perpendicular x and y dimensions.
Static friction matches applied force until the breaking point (μsFN).
Centripetal force is a net force, not a distinct type of force.
End of Unit 2 Study Guide.