AP Physics 1 Notes

Vectors have magnitude + direction Scalars have magnitude, but no direction Component vectors can be found with Sin and cos of the angle and the horizontal/vertical and the magnitude of the vector. Distance: Scalar, path traveled Displacement: Vector, straight-line distance Speed: distance / time, Scalar Velocity: displacement / time, Vector Acceleration: Δvelocity / Δtime, Vector Graphs Position (m) vs. time (s) Slope = velocity Velocity (m/s) vs. time (s) Slope = acceleration Area under curve = Δposition Acceleration (m/s²) vs. time (s) Area under curve = Δvelocity Object in graph is in free fall ay = -g = -9.81 m/s² acceleration (m/s²) velocity (m/s) position (m) g (font) = +9.81 m/s² Uniformly Accelerated Equations Vf = Vo + at Δx = Vot + 1/2at² Vf² = Vo² + 2aΔx Δx = (Vf + Vo)/2 * Δt Projectile motion x-direction ax = 0 constant velocity Vx = x y-direction ay = -g = -9.81 m/s² UAM equations t is the same for both (Scalar) free fall t = 2VoSinθ / g Relative motion vector diagrams vector components make right triangles find resultant vector Center of mass (qualitatively) Center of mass In translational motion, the whole object or system of objects is treated at its center of mass. Motion - Changing position or location Frame of reference - a set of coordinates that can be used to determine positions of objects. Motion Diagrams Constant Speed [Diagram of equally spaced dots in a straight line] Constant acceleration [Diagram of dots increasingly spaced apart in a straight line] Experimental Design List of equipment Procedure for data collection Proper analysis of data Lab Equipment Distance: meterstick, ruler Time: stopwatch, photogate, video camera with known frame rate Velocity: photogate, motion detector Linearizing Graphs Aim to get a higher R^2 value and more linear model Change on axis to get a more linear fit Instantaneous speed = average speed in an accelerating system Center of mass (m1x1 + m2x2 + ...)/(m1 + m2 + ...) (m1y1 + m2y2 + ...)/(m1 + m2 + ...) Flipping Physics Dynomics Review Inertial mass: measure of inertia; resistance of an object to acceleration. Gravitational mass: identical to inertial mass, used to determine weight, experimentally. Newton's Laws of Motion An object at rest will remain at rest and an object in motion will maintain a constant velocity unless acted upon by a net external force. (Newton's First Law) F = ma (Newton's Second Law) Identify objects and direction. a = ΣF/m Free Body Diagrams Ex: Draw a FBD for a man pushing on a book against a wall. Fa, Fn, Fg (no components on original FBD, only the resultant forces) Force of Gravity Weight Downwards Fg = mg Normal Force Always a push, perpendicular to surface Forces measured in Newtons, N = kg*m/s^2 Force of Friction Parallel to surface, opposes motion, but is independent of Fa Static friction: non-moving; surfaces don't slide relative to one another Kinetic friction: moving; surfaces are sliding relative to one another Fk = Mk * Fn Fsc ≤ Ms * Fn Fsf_max = Ms * Fn For same 2 surfaces, Ms > Mk ③ For every force object one applies on object two, there is an equal but opposite force that object two applies on object one where both forces are vectors F12 = -F21 Newton's Third Law Newton's Third Law Force Pair 2 different objects simultaneous Inclines Fg|| = mg * sinθ = force down incline Fg⊥ = mg * cosθ - Fn Translation equilibrium ΣF = 0 ⇒ a = 0 Percent Error = (observed - accepted) / accepted * 100 Acceleration: change in state of motion Contact Force: a force that occurs when 2 interacting objects touch Field Force: Two objects that are interacting without touching Applied Force: Force applied on an object by a different object. System: object or group of objects being analyzed. Everything outside is called the environment. Force of tension: the force transmitted through a rope, cable, string, or wire pulled taut by forces acting on both sides. Hooke's Law: Fs = -kx Displacement is opposite in direction to the spring force Restoring Force: force that always brings an object back to equilibrium position. Elastic Limit: maximum displacement a spring can allow before permanent deformation. Translational Equilibrium: ΣF on object = 0 Apparent Weight: the upward normal force on an object Elevator Scenario: If ay > 0 -> Fn > Fg If ay = 0 -> Fn = Fg If ay < 0 -> Fn < Fg If ay = -g -> Fn = 0 -> apparent weightlessness Atwood Machine: a = (m2 - m1) / (m1 + m2) * g Modified Atwood Machine: a = (m1g - M2mgcosθ) / (m1 + m2) Angular velocity ω = Δθ / Δt measured in rad/s or rev/min 1 rev = 360° = 2π rad Angular acceleration α = Δω / Δt measured in rad/s² Uniformly Angularly Accelerated Motion Equations ωf = ω₀ + αt Δθ = ω₀t + 1/2 αt² ωf² = ω₀² + 2αΔθ Δθ = (ωf + ω₀)/2 * Δt Uniform circular motion: when an object is rotating and α = 0 Tangential velocity: linear velocity of object moving in a circle Vt = rω ω must be in rad/s Centripetal Acceleration: ac = V²/r = rω² always directed inward Centripetal Force Fc = mv²/r = mac not a new force, ΣF in the in-direction never in a free body diagram in-direction is positive, out-direction is negative. Period - time for one full revolution T = 1/f = 2π/ω Measured in seconds or seconds/cycle Frequency - cycles traveled per second f = 1/T Measured in cycles/sec = Hertz Conical Pendulum Example T_pendulum = 2π√(L/g) Free Body Diagram F_Ty F_Tx F_g ΣF_in = F_Tx = ma_c = mv²/r Vt = rw = Δx/Δt = 2πr/T Centripetal Force in Vertical Path T - mg (lightest) For roller coaster questions, replace T with FN T = Fc + mg (heaviest)