AP Physics B Study Guide: Semester 1
LAWS & PRINCIPLES & THEORIES: Newton’s Laws: First Law of Motion: When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force. Second Law of Motion: The vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration vector a of the object: F = ma. Third Law of Motion: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.
Kepler’s Laws of Planetary Motion: 1. All planets will follow an elliptical path with the sun at one focus. 2. Conservation of angular motion: Lo = L’ “Equal Area - Equal Time” p = mv L = Iω where I = nmr2 with n determined by the parallel axis theorem 3. T2 ∝ r3
Newton’s Law of Gravitation: Fg = Gm1m2/R2 G = 6.67 × 10−11 Nm2/kg2
Fluid Principles: 1. Archimedes: Buoyant Force on an object is equal to the Weight of the fluid displaced. 2. Bernoulli’s: Pressure is inversely proportional to fluid velocity. 3. Pascal’s: Pressure in an enclosed fluid is transmitted without change.
Thermodynamics: Zeroth Law of Thermodynamics: Thermal Equilibrium is determined by temperature. Two objects are at thermal equilibrium at the same temperature. If A is in equilibrium with B and C is in equilibrium with B, A and C will be at equilibrium if they are in thermal contact. First Law of Thermodynamics: Conservation of energy. Second Law of Thermodynamics: When objects of different temperatures are in contact, flow of heat goes from high to low temperature. Third Law of Thermodynamics: The entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero. However, 0K is impossible.
Gas Laws: Boyle’s Law: P ∝ 1/V with constant T - Please add the graphs and the specific qualities about each graphs (Q=0, Work= 0 etc) Gay-Lussac’s Law: T∝ P with constant V Charles’s Law: T∝V with constant P
Kinetic Theory: Molecules in a gas, when colliding, ALWAYS bounce elastically (elastic collisions). Therefore, KE, and thus T, is preserved. Also, Pressure is directly proportional to Kinetic Energy. As Temperature increases, so does KE.
GENERAL UNITS: N: kgm/s2 J: kgm2/s2 or Nm Rodinos: kgm/s Spring Constant: N/m Gravitational Constant: _Gc Real Gas Constant: _Rc Pa: N/m2 or kg/(ms2)
UNIT 1- 1D Motion & UNIT 2- 2D Motion: v=Δd/Δt a=Δv/Δt Big Three: d=vot+1/2at2 v2=vo2+2ad v=vo+at
UNIT 3- Newton’s Laws: Σ F=ma
Weight: W=mg Hooke’s Law (Springs): Fs= -kx x: distance from EQ Friction: f=μN Normal Force: mgcosθ
UNIT 4- Energy and SHM: Work: W=Fdcosθ Force must be in direction of displacement Kinetic Energy: KE=1/2mv2 Gravitational Potential Energy: PEg=mgh Spring Potential Energy: PEs=1/2kx2
Mechanical Energy: E=Σ of U+KE Work-Energy Theorem: Wtotal = ∆KE Conservative Work: Wc=-∆U Nonconservative Work: Wnc=∆E Energy is conserved: Ei=Ef
SHM: Oscillatory Motion: 1/2kA2 A: amplitude; maximum displacement from the equilibrium position. v max when at EQ Varies per problem (look back at your notes for this one): Horizontal: a=kx/m Vertical: amax=kA/m vmax=A√(k/m) x=A v’=√((kA2-kx’2)/m)v Period (Spring): Ts=2π√(m/k)
Power: P=Fv or W/t
UNIT 5- Momentum: Every action has an equal and opposite reaction: po=p’ Pa+Pb=(Pa+Pb)’ 0=Pa’+-Pb’ 0=0 Momentum (mass in motion): p=mv “Rodinos” Impulse in J: change in momentum= mdeltav=Ft Linear momentum is CONSERVED
Elastic Collisions: KEf=KEi Bounce Inelastic Collisions: KEf=/=KEi; Real World
v2-v1=vo (Speed of Separation = Speed of Approach) v1’=[(m1-m2)/(m1+m2)]vo v2’=[(2m1)/(m1+m2)]vo Elastic Situation #1: Masses equal Velocities switch for initial and after Elastic Situation #2: First mass smaller than second First mass sent back Second velocity approx 0 First velocity approx -v Elastic Situation #3: First mass bigger than second First velocity approx same Second velocity 2vo
UNIT 6- Circular Motion: Sum of Centripetal Forces: Σ Fc=mac Centripetal Acceleration: ac=v2/R Constant speed Centripetal Force: mv2/R=Fc If constant speed: m4π2R/T2 m4π2Rf2 Frequency: f=1/T in Hz or rpm Centripetal Forces always act toward center and cause change in direction Banked roads: Tilted towards center. Normal force exerted by the road contributes to centripetal. In a skid, friction is kinetic, which resists movement. The wheel and road cannot hold each other (not enough friction) in a side turn, and thus force is needed. If there is not enough friction, the car skids and thus spins as it slides, and thus does not maintain consistent movement (no longer has control). Static friction can point towards the center, and thus act as a centripetal force, but kinetic friction cannot. Newton’s Law of Gravitation: Fg=Gm1m2/R2 G=6.674210-11m3/(kgs2) R= distance BETWEEN CENTERS
Arc Length: s=rθ Period: T=2π/ω θ: reference point to the axis, then the axis to a spot. If θ>0, counterclockwise If θ<0, clockwise Angular Velocity: ωav=Δθ/Δt ω=2π/T=2πf radians per second. Convert from revolutions. If ω>0, counterclockwise If ω<0, clockwise Angular Acceleration: αav=Δω/Δt If ω becomes more positive, α is positive Tangential Speed: vt=rω Centripetal Acceleration: acp=rω2=mv2/R Tangential Acceleration: at=rα Change in tangential speed, while centripetal acceleration is a change of direction of motion Right angle to acp Big Three: θ=ωot+1/2αt2 ω2=ωo2+2αθ
Moment of Inertia (Rotational Inertia): I=Σmiri2 in kgm2 MR2 for a hoop ½MR2 for a disk Rotational Kinetic Energy: KE=½Iω2 KE of Rolling Motion: ½mv2+½Iω2 KE=1/2mv2[1+(I/MR2)] Depends on shape and mass distribution Keep in mind LINEAR and ROTATIONAL Motions In the case of a wheel, pure rotational motion would have the top move at v=rω. For translational motion, it also moves at v=rω,. So, in a rolling motion, the top moves at v=2rω. Period T of a Planet: T= (2π/√(GMs))r3/2 Torque (Rotational Force): ΣT=Iα T=FRsinθ: Valid only when Force is tangential to a circle of radius R ΣT=ΔL/Δt T>0, counterclockwise angular acceleration (but be consistent with the direction of motion) T<0, clockwise acceleration (but be consistent with the direction of motion) (Check your notes for the rotational pulley questions!) Objects that are uniform (such as a meter stick) have total mass at any point... the force (weight) is placed on the midpoint Angular Momentum: L=Iω L=rpsinθ or mvr Center of Mass: m1x1=m2x2 Angular Momentum is conserved: Lf=Li