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It covers vector math (magnitude, dot and cross products), quadratic solutions, calculus links for derivatives and integrals, and fundamental motion in one and two/three dimensions. The sheet continues with Newton’s laws, friction, work, kinetic and potential energy, momentum and impulses, collisions, rotational kinematics, torque and angular momentum, static equilibrium, fluid mechanics, and gravitation constants plus orbital relations and escape 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topics are included in the NJIT Physics 111 formula sheet?","Question",{"text":102,"@type":103},"It includes vector operations, kinematics in one and two/three dimensions, Newton’s laws, friction, work and energy, momentum and collisions, rotational dynamics, static equilibrium, fluid mechanics, and gravitation.","Answer",{"name":105,"@type":100,"acceptedAnswer":106},"How does the sheet present motion formulas?",{"text":107,"@type":103},"It lists displacement, velocity, and acceleration relationships for constant velocity and constant acceleration cases, including projectile motion and position/velocity vector forms.",{"name":109,"@type":100,"acceptedAnswer":110},"What gravitation relationships are provided?",{"text":111,"@type":103},"It provides the gravitational constant G, Earth mass and radius, gravitational force and potential energy, orbital period and orbit speed relations, Kepler’s law form, and escape velocity.","https://schema.org",{"og:url":78,"og:type":114,"og:title":59,"og:site_name":86,"og:description":61},"article",{"robots":116,"canonical":78},"index,follow",{"doc_id":118,"site_id":56},573091,1791932016,{"code":4,"msg":5,"data":121},{"doc_id":118,"user_id":122,"nickname":83,"user_avatar":123,"doc_module":9,"category_id":35,"category_name":36,"doc_title":59,"doc_description":61,"doc_content":124,"file_id":125,"file_url":126,"file_type":127,"file_size":128,"view_count":4,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":73,"language":129,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":130,"faqs":131,"seo_title":132,"seo_description":61,"update_tm":119,"read_time":9},137451207643,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","NJIT Physics 111 Formula Sheet  \n Chapter 1:Vectors and Mathematics Formulas   \nVector magnitude: Vector direction: Dot Product:  \n| ⃗A| = qA2x + A2y or qA2x + A2y + A2z tan θ = AAyx ⃗A · ⃗B = AxBx + Ay By + Az Bz = | ⃗A|| ⃗B| cosθ  \nCross Product: ˆi × ˆj = ˆk ˆj × ˆk = ˆi ˆk × ˆi = ˆj  \nˆi × ˆi = ˆj × ˆj = ˆk × ˆk = 0  \n⃗A × ⃗B = (Ay Bz − Az By)ˆi+ (Az Bx − Ax Bz)ˆj +(Ax By − Ay Bx) ˆk  \n| ⃗A × ⃗B| = | ⃗A|| ⃗B| sinθ    \nQuadratic formula: ax2 + bx + c = 0, x = 􀀀−b ±√b2 − 4ac 􀀁/(2a)  \nDerivatives, Integrals: ~~ d~~dttn = ntn−1 and´ tn dt = n1 tn+1 Circumference: C = 2πr  \nSphere area, volume: A = 4πr2 , V = ~~4~~3πr3  \nChapter 2: One-Dimensional Motion  \nDisplacement: ∆x = xf − x0  \nConstant velocity: xf = x0 + vt or ∆x = vt  \nKinematics: vf = v0 + at  \n∆x = v0t + ~~1~~2at2  \nv2f = v20 + 2a∆x  \nvf + v0 = 2∆x/t  \n∆x = vft − ~~1~~2at2  \nVelocity: vavg = (xf − x0 )/ (tf − t0 ), v (t) = dx/dt  \nAcceleration: aavg = (vf − v0 )/ (tf − t0 ), a (t) = dv/dt Acceleration due to gravity: g = 9 .8 m/s2  \nChapter 3: Two-and Three-Dimensional Motion  \nPosition vector: ⃗r = xˆi + yˆj + z ˆk  \nAverage velocity ⃗vavg = (r⃗f − ⃗r0 )/ (tf − t0 ) Instantaneous velocity: ⃗v(t) = d⃗r/dt  \nAverage acceleration: ⃗aavg = (⃗vf − ⃗v0 )/ (tf − t0 ) Instantaneous acceleration: ⃗a(t) = d⃗v/dt  \nProjectile range: R = v 2 sin(2θ)/g Radial acceleration: arad = v 2 /r = 4π2 r/T2  \nChapter 4: Newton’s Laws of Motion  \nFirst Law: ⃗Fnet = 0 ←→ ⃗v = constant Second Law: ⃗Fnet = m⃗a  \nThird Law: ⃗F12 = − ⃗F21  \nChapter 5: Applying Newton’s Laws  \nKinetic and static friction: fk = µkFN and fs ≤ µsFN Normal force: FN = mg on horizontal surface,  \nFN = mg cosθ on incline  \nChapter 6: Work and Kinetic Energy  \nWork done by a constant force: W = ⃗F · ⃗s = Fs cosθ  \nKinetic energy: K = ~~1~~2mv 2  \nWork-energy theorem: Wtot = K2 − K1 = ∆K Work by a non-constant force: Wa→b = ´ba ⃗F · d⃗r  \nPower: P = ∆W/∆t or dW/dt P = ⃗F · ⃗v  \nChapter 7: Potential Energy and Energy Conservation  \nHooke’s Law: Fx = −k(xf − x0 )  \nWork done by a spring: W = ~~1~~2k (x2f − x20)  \nWork done by gravity: W = −mg∆y Gravitational potential energy: Ug = mgh  \nElastic potential energy: UE = ~~1~~2kx2  \nConservation: (K + Ug + UE )0 + Wother = (K + Ug + UE )f Force and Potential Energy: Fx = −dU(x)/dx  \n Chapter 8: Momentum, Impulse, and Collisions   \nMomentum: p⃗ = m⃗v  \nForce and momentum: ⃗F = ∆⃗p/∆t or d⃗p/dt  \nImpulse: ⃗J= ∆p⃗ = m∆⃗v = ⃗Favg ∆t  \n⃗J = ´tt12 ⃗F(t) dt  \nConservation: mA ⃗vA + mB ⃗vB + ... = mA ⃗vA ′ + mB ⃗vB ′ + ...  \n(⃗vA ′, ⃗vB ′ are post-collision velocities)  \nCompletely inelastic collision: mA ⃗vA + mB ⃗vB = (mA + mB )⃗vf  \n1-D Elastic collisions: vA + v′A = vB + v′B  \nCenter of mass: ⃗rCM = (m1 ⃗r1 + m2 ⃗r2 + ... )/ (m1 + m2 + ... )  \nChapter 9: Rotation of Rigid Bodies  \nAngular displacement: ∆θ = θf − θ0  \nConstant velocity: θf = θ0 + ωt or ∆θ = ωt  \nKinematics: ωf = ω0 + αt ∆θ = ω0t + ~~1~~2αt2 ω2f = ω20 + 2α∆θωf + ω0 = 2∆θ/t  \nVelocity: ωavg = (θf − θ0 )/ (tf − t0 ), ω (t) = dθ/dt  \nAcceleration: αavg = (ωf − ω0 )/ (tf − t0 ), α (t) = dω/dt Angular → tangential: ∆s = r∆θ , vtan = rω , atan = rα  \nRadial acceleration: arad = rω 2 Rotational kinetic energy: Krot = ~~1~~2Iω 2  \nCM Moment of Inertia: Point mass, mr2 . Disk, ~~1~~2mR2 . Ring, mR2 .  \nSpherical shell, ~~2~~3mR2 . Sphere, ~~2~~5mR2 . Rod (about center), 1~~1~~2 mL2  \nParallel axis theorem: I = ICM + md2  \n\n| \u003Cbr>Chapter 10: Dynamics of Rotational Motion |  |\n| --- | --- |\n| Torque (magnitude):\u003Cbr>Torque (vector): Newton’s 2nd Law: Translation/rotation:\u003Cbr>No-slip condition: Work done by constant torque:\u003Cbr>Work-energy theorem: Angular momentum:\u003Cbr>Conservation of angular momentum: | τ = rF sinθ⃗τ = ⃗r × ⃗F\u003Cbr>τnet = Iα K = ~~1~~2mv2cm + ~~1~~2Icmω 2 vcm = Rω\u003Cbr>W = τ∆θ\u003Cbr>Wtot = ~~1~~2Iω2f − ~~1~~2Iω20 ⃗L = ⃗r × p⃗ (particle)\u003Cbr>⃗L = I⃗ω (rigid body rotating about axis) IAωA + IB ωB = I′Aω′A + I′Bω′B (primes indicate ‘final’) |\n\nChapter 11: Static Equilibrium  \nStatic equilibrium conditions: ⃗Fnet = 0  \n⃗τ","cbCaiuJY0JmKcmWC","https://ap.wps.com/l/cbCaiuJY0JmKcmWC","pdf",163584,"English","# Chapter 1: Vectors and Mathematics Formulas\n## Chapter 2: One-Dimensional Motion\n## Chapter 3: Two-and Three-Dimensional Motion\n## Chapter 4: Newton’s Laws of Motion\n## Chapter 5: Applying Newton’s Laws\n## Chapter 6: Work and Kinetic Energy\n## Chapter 7: Potential Energy and Energy Conservation\n## Chapter 8: Momentum, Impulse, and Collisions\n## Chapter 9: Rotation of Rigid Bodies\n## Chapter 10: Dynamics of Rotational Motion\n## Chapter 11: Static Equilibrium\n## Chapter 12: Fluid Mechanics\n## Chapter 13: Gravitation","[{\"question\":\"What topics are included in the NJIT Physics 111 formula sheet?\",\"answer\":\"It includes vector operations, kinematics in one and two/three dimensions, Newton’s laws, friction, work and energy, momentum and collisions, rotational dynamics, static equilibrium, fluid mechanics, and gravitation.\"},{\"question\":\"How does the sheet present motion formulas?\",\"answer\":\"It lists displacement, velocity, and acceleration relationships for constant velocity and constant acceleration cases, including projectile motion and position/velocity vector forms.\"},{\"question\":\"What gravitation relationships are provided?\",\"answer\":\"It provides the gravitational constant G, Earth mass and radius, gravitational force and potential energy, orbital period and orbit speed relations, Kepler’s law form, and escape velocity.\"}]","NJIT Physics 111 Formula Sheet - Chapter 1 to Chapter 13 Physics Formulas | PDF"]