AP Physics 1
Advanced Placement Physics 1: Algebra-Based, aligned with the College Board CED (2024-25 redesign). Covers kinematics, dynamics, work/energy/power, linear momentum, torque and rotational dynamics, rotational energy and angular momentum, oscillations, and fluids.
Ämne: Fysik · Nivå: Gymnasium (16–19) · 411 kort
Innehåll
- Kinematics is the branch of mechanics that describes motion (position, velocity, acceleration) without considering the forces that cause it. AP Physics 1 treats motion in one and two dimensions using algebra-based equations for constant acceleration.
- Displacement Δx is a vector from initial to final position; distance is the scalar path length traveled. A runner who goes 400 m around a track and returns to the start has 400 m distance but 0 m displacement.
- Average velocity is displacement divided by time: v_avg = Δx/Δt. Instantaneous velocity is the limit as Δt → 0, which graphically equals the slope of the position-vs-time curve at that instant.
- Average acceleration is the change in velocity over time: a_avg = Δv/Δt. SI units are m/s². Acceleration is a vector and points in the direction of Δv, not necessarily in the direction of motion.
- On a position-vs-time graph, the slope gives velocity. On a velocity-vs-time graph, the slope gives acceleration and the area under the curve gives displacement. These graphical relationships work for any motion, not just constant acceleration.
- The five kinematic equations for constant acceleration: v = v₀ + at; Δx = v₀t + ½at²; v² = v₀² + 2aΔx; Δx = ½(v₀ + v)t; Δx = vt − ½at². Each omits one variable, letting you choose based on what's known and unknown.
- Free fall is motion under gravity alone, with no air resistance. Near Earth's surface all objects in free fall accelerate downward at g ≈ 9.8 m/s², independent of mass. AP Physics 1 commonly approximates g = 10 m/s² for quick estimates.
- At the peak of a vertical throw, instantaneous velocity is zero but acceleration is still g downward. The object slows to a stop on the way up, then speeds up on the way down at the same rate.
- Projectile motion decomposes into independent horizontal and vertical motions. Horizontally: aₓ = 0 and vₓ = v₀ₓ stays constant. Vertically: a_y = −g and v_y changes by gt. Time aloft links the two axes.
- For a projectile launched at angle θ with speed v₀ on level ground: range R = v₀² sin(2θ)/g. Maximum range occurs at θ = 45°. Complementary angles (e.g., 30° and 60°) give the same range but different maximum heights.
- A projectile launched horizontally from a height h falls for t = √(2h/g) regardless of its horizontal speed. A bullet fired horizontally and a bullet dropped from the same height hit the ground simultaneously.
- A reference frame is the coordinate system from which motion is measured. Velocities transform between frames by vector addition: v_AC = v_AB + v_BC, where v_AC is A's velocity relative to C, v_AB relative to B, and v_BC is B's velocity relative to C.
- A scalar quantity has only magnitude (mass, time, speed, energy, temperature). A vector has both magnitude and direction (displacement, velocity, acceleration, force, momentum). Vectors are added tip-to-tail or component-wise.
- To resolve a vector v at angle θ from horizontal: vₓ = v cosθ, v_y = v sinθ. Magnitude from components: v = √(vₓ² + v_y²). Direction: θ = arctan(v_y/vₓ). Always be careful with signs and quadrants.
- When velocity and acceleration point in the same direction, the object speeds up. When they point in opposite directions, the object slows down. Negative acceleration does not mean slowing down — it depends on the velocity's sign too.
- A position-vs-time graph that curves upward (concave up) indicates positive acceleration; concave down indicates negative acceleration. A straight line indicates constant velocity (a = 0).
- Speed is the magnitude of velocity — always non-negative. A car moving at 30 m/s east and 30 m/s west have the same speed but opposite velocities. Average speed = total distance / total time; average velocity = displacement / time.
- Galileo's principle of inertia: in the absence of friction, a horizontally moving object will continue at constant velocity indefinitely. This insight, contrary to Aristotle, set up Newton's first law and shifted physics from describing motion to explaining changes in motion.
- Uniform circular motion has constant speed but changing velocity direction, so there is a non-zero acceleration. The acceleration always points toward the center of the circle and has magnitude a_c = v²/r (centripetal acceleration).
- Newton's first law (law of inertia): an object at rest stays at rest, and an object in motion continues at constant velocity, unless acted on by a net external force. Inertia is the resistance of an object to changes in its state of motion, and is measured by mass.
- Newton's second law: F_net = ma. The net (vector sum of) force on an object equals its mass times its acceleration. The acceleration is in the same direction as the net force. SI unit of force: newton (N) = kg·m/s².
- Newton's third law: when object A exerts a force on object B, object B exerts an equal-magnitude, opposite-direction force on A. These action-reaction pairs act on different objects, so they never cancel out on a single object.
- A free-body diagram (FBD) shows only the forces acting on a single object, drawn as arrows originating from that object. Internal forces and forces the object exerts on others are excluded. The FBD is the foundation for applying Newton's second law.
- Mass (kg) is a measure of inertia and is independent of location. Weight (N) is the gravitational force on an object: W = mg. A 1 kg mass weighs about 9.8 N on Earth but only about 1.6 N on the Moon.
- The normal force F_N is the contact force from a surface, perpendicular to the surface, that prevents an object from passing through it. On a horizontal surface with no vertical acceleration, F_N = mg. On an incline of angle θ, F_N = mg cosθ.
- Static friction prevents relative motion between surfaces and adjusts in magnitude up to a maximum f_s,max = μ_s F_N. Kinetic friction acts on surfaces already sliding and is approximately constant: f_k = μ_k F_N. Typically μ_s > μ_k.
- On a frictionless incline of angle θ, the gravity component parallel to the surface is mg sinθ, and the component perpendicular is mg cosθ. The block accelerates down the incline at a = g sinθ regardless of its mass.
- Tension is the pulling force transmitted through a rope, string, or cable. An ideal (massless, inextensible) rope has the same tension throughout. An ideal pulley simply changes the direction of tension without changing its magnitude.
- An Atwood machine has two masses m₁ and m₂ connected by a string over an ideal pulley. The system accelerates at a = (m₁ − m₂)g / (m₁ + m₂) and the tension is T = 2m₁m₂ g / (m₁ + m₂).
- Newton's law of universal gravitation: F = Gm₁m₂/r², where G ≈ 6.674×10⁻¹¹ N·m²/kg² and r is the center-to-center distance. The force is attractive and acts along the line connecting the two masses.
- Near Earth's surface, g ≈ 9.8 m/s² because GM_E/R_E² evaluates to that value, where M_E ≈ 5.97×10²⁴ kg and R_E ≈ 6.37×10⁶ m. Gravity weakens with the square of distance from Earth's center.
- A system is in translational equilibrium when the net force on it is zero. This includes both static equilibrium (at rest) and dynamic equilibrium (constant velocity). Equilibrium does not mean motionless — it means non-accelerating.
- A force is centripetal if and only if it acts toward the center of a circular path. "Centripetal" describes the role a force plays, not a new type of force. Gravity, tension, normal force, or friction can all serve as the centripetal force depending on context.
- For uniform circular motion at speed v on radius r, the net inward force equals F_c = mv²/r. There is no outward "centrifugal force" in an inertial frame — the feeling of being thrown outward is just inertia opposing the inward acceleration.
- An object in apparent weightlessness inside a freely falling elevator experiences zero normal force but still has gravity acting on it. Astronauts in orbit are weightless in the same sense — they are in continuous free fall around Earth.
- Apparent weight is the normal force from a supporting surface. In an elevator accelerating upward at a, apparent weight = m(g + a) (you feel heavier). Accelerating downward at a < g, apparent weight = m(g − a) (you feel lighter).
- Work is energy transferred to or from an object by a force acting over a displacement: W = F·d·cosθ, where θ is the angle between the force and the displacement. SI unit of work: joule (J) = N·m.
- Work is zero when force is perpendicular to displacement (θ = 90°). Examples: gravity does no work on a horizontally sliding block; the centripetal force does no work in uniform circular motion; the normal force does no work as a block slides on a flat surface.
- Translational kinetic energy is KE = ½mv². It is a scalar, always non-negative, depends on the reference frame, and on speed (not velocity direction). Doubling the speed quadruples the kinetic energy.
- The work-energy theorem: the net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½mv² − ½mv₀². It is equivalent to Newton's second law combined with kinematics.
- Gravitational potential energy near Earth's surface is PE_g = mgh, where h is height measured from a chosen reference level. Only differences in PE matter physically; the choice of reference level is arbitrary.
- Elastic potential energy stored in a spring of stiffness k displaced x from equilibrium is PE_s = ½kx². It is always non-negative and is independent of whether the spring is stretched or compressed.
- Hooke's law: the restoring force of an ideal spring is F = −kx, where k is the spring constant (N/m) and x is the displacement from equilibrium. The minus sign indicates the force always opposes the displacement.
- A conservative force is one whose work between two points is path-independent, equivalent to saying it can be associated with a potential energy. Gravity and ideal spring forces are conservative; friction and air drag are non-conservative (dissipative).
- Conservation of mechanical energy: when only conservative forces do work, KE + PE = constant. A pendulum's bob exchanges PE_g and KE at every point of its swing while their sum remains the same (ignoring air friction).
- When non-conservative forces (friction, air drag) act, mechanical energy decreases: ΔKE + ΔPE = W_nc, where W_nc is the work done by non-conservative forces (typically negative). The "lost" energy is converted to thermal energy or sound.
- Power is the rate of energy transfer: P_avg = W/Δt, P_inst = dW/dt. For a constant force moving an object at constant velocity, P = Fv (or P = Fv cosθ if the force is not parallel to v). SI unit: watt (W) = J/s.
- The work done by gravity on an object lowered through height h is W_grav = +mgh (positive when motion is downward). Going up, gravity does negative work −mgh. The result depends only on the change in height, not the path taken.
- On a force-vs-position graph, the area between the curve and the position axis equals the work done by that force. For a linear spring force F = kx, the area is the triangle giving W = ½kx², matching the elastic PE stored.
- Energy comes in many forms: mechanical (kinetic + potential), thermal, chemical, nuclear, electromagnetic, sound, etc. The first law of thermodynamics generalizes conservation of energy: total energy is conserved across all forms in any isolated system.