NJIT Physics 111 Formula Sheet - Chapter 1 to Chapter 13 Physics Formulas

Oct 13, 2026

A compact physics reference sheet compiling core formulas for NJIT Physics 111 across thirteen topics. 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 velocity.

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Pages2

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Chapter 1: Vectors and Mathematics Formulas

Chapter 2: One-Dimensional Motion

Chapter 3: Two-and Three-Dimensional Motion

Chapter 4: Newton’s Laws of Motion

Chapter 5: Applying Newton’s Laws

Chapter 6: Work and Kinetic Energy

Chapter 7: Potential Energy and Energy Conservation

Chapter 8: Momentum, Impulse, and Collisions

Chapter 9: Rotation of Rigid Bodies

Chapter 10: Dynamics of Rotational Motion

Chapter 11: Static Equilibrium

Chapter 12: Fluid Mechanics

Chapter 13: Gravitation

NJIT Physics 111 Formula Sheet Chapter 1:Vectors and Mathematics Formulas Vector magnitude: Vector direction: Dot Product: | ⃗A| = qA2x + A2y or qA2x + A2y + A2z tan θ = AAyx ⃗A · ⃗B = AxBx + Ay By + Az Bz = | ⃗A|| ⃗B| cosθ Cross Product: ˆi × ˆj = ˆk ˆj × ˆk = ˆi ˆk × ˆi = ˆj ˆi × ˆi = ˆj × ˆj = ˆk × ˆk = 0 ⃗A × ⃗B = (Ay Bz − Az By)ˆi+ (Az Bx − Ax Bz)ˆj +(Ax By − Ay Bx) ˆk | ⃗A × ⃗B| = | ⃗A|| ⃗B| sinθ Quadratic formula: ax2 + bx + c = 0, x = 􀀀−b ±√b2 − 4ac 􀀁/(2a) Derivatives, Integrals: ~~ d~~dttn = ntn−1 and´ tn dt = n1 tn+1 Circumference: C = 2πr Sphere area, volume: A = 4πr2 , V = ~~4~~3πr3 Chapter 2: One-Dimensional Motion Displacement: ∆x = xf − x0 Constant velocity: xf = x0 + vt or ∆x = vt Kinematics: vf = v0 + at ∆x = v0t + ~~1~~2at2 v2f = v20 + 2a∆x vf + v0 = 2∆x/t ∆x = vft − ~~1~~2at2 Velocity: vavg = (xf − x0 )/ (tf − t0 ), v (t) = dx/dt Acceleration: aavg = (vf − v0 )/ (tf − t0 ), a (t) = dv/dt Acceleration due to gravity: g = 9 .8 m/s2 Chapter 3: Two-and Three-Dimensional Motion Position vector: ⃗r = xˆi + yˆj + z ˆk Average velocity ⃗vavg = (r⃗f − ⃗r0 )/ (tf − t0 ) Instantaneous velocity: ⃗v(t) = d⃗r/dt Average acceleration: ⃗aavg = (⃗vf − ⃗v0 )/ (tf − t0 ) Instantaneous acceleration: ⃗a(t) = d⃗v/dt Projectile range: R = v 2 sin(2θ)/g Radial acceleration: arad = v 2 /r = 4π2 r/T2 Chapter 4: Newton’s Laws of Motion First Law: ⃗Fnet = 0 ←→ ⃗v = constant Second Law: ⃗Fnet = m⃗a Third Law: ⃗F12 = − ⃗F21 Chapter 5: Applying Newton’s Laws Kinetic and static friction: fk = µkFN and fs ≤ µsFN Normal force: FN = mg on horizontal surface, FN = mg cosθ on incline Chapter 6: Work and Kinetic Energy Work done by a constant force: W = ⃗F · ⃗s = Fs cosθ Kinetic energy: K = ~~1~~2mv 2 Work-energy theorem: Wtot = K2 − K1 = ∆K Work by a non-constant force: Wa→b = ´ba ⃗F · d⃗r Power: P = ∆W/∆t or dW/dt P = ⃗F · ⃗v Chapter 7: Potential Energy and Energy Conservation Hooke’s Law: Fx = −k(xf − x0 ) Work done by a spring: W = ~~1~~2k (x2f − x20) Work done by gravity: W = −mg∆y Gravitational potential energy: Ug = mgh Elastic potential energy: UE = ~~1~~2kx2 Conservation: (K + Ug + UE )0 + Wother = (K + Ug + UE )f Force and Potential Energy: Fx = −dU(x)/dx Chapter 8: Momentum, Impulse, and Collisions Momentum: p⃗ = m⃗v Force and momentum: ⃗F = ∆⃗p/∆t or d⃗p/dt Impulse: ⃗J= ∆p⃗ = m∆⃗v = ⃗Favg ∆t ⃗J = ´tt12 ⃗F(t) dt Conservation: mA ⃗vA + mB ⃗vB + ... = mA ⃗vA ′ + mB ⃗vB ′ + ... (⃗vA ′, ⃗vB ′ are post-collision velocities) Completely inelastic collision: mA ⃗vA + mB ⃗vB = (mA + mB )⃗vf 1-D Elastic collisions: vA + v′A = vB + v′B Center of mass: ⃗rCM = (m1 ⃗r1 + m2 ⃗r2 + ... )/ (m1 + m2 + ... ) Chapter 9: Rotation of Rigid Bodies Angular displacement: ∆θ = θf − θ0 Constant velocity: θf = θ0 + ωt or ∆θ = ωt Kinematics: ωf = ω0 + αt ∆θ = ω0t + ~~1~~2αt2 ω2f = ω20 + 2α∆θωf + ω0 = 2∆θ/t Velocity: ωavg = (θf − θ0 )/ (tf − t0 ), ω (t) = dθ/dt Acceleration: αavg = (ωf − ω0 )/ (tf − t0 ), α (t) = dω/dt Angular → tangential: ∆s = r∆θ , vtan = rω , atan = rα Radial acceleration: arad = rω 2 Rotational kinetic energy: Krot = ~~1~~2Iω 2 CM Moment of Inertia: Point mass, mr2 . Disk, ~~1~~2mR2 . Ring, mR2 . Spherical shell, ~~2~~3mR2 . Sphere, ~~2~~5mR2 . Rod (about center), 1~~1~~2 mL2 Parallel axis theorem: I = ICM + md2 |
Chapter 10: Dynamics of Rotational Motion | | | --- | --- | | Torque (magnitude):
Torque (vector): Newton’s 2nd Law: Translation/rotation:
No-slip condition: Work done by constant torque:
Work-energy theorem: Angular momentum:
Conservation of angular momentum: | τ = rF sinθ⃗τ = ⃗r × ⃗F
τnet = Iα K = ~~1~~2mv2cm + ~~1~~2Icmω 2 vcm = Rω
W = τ∆θ
Wtot = ~~1~~2Iω2f − ~~1~~2Iω20 ⃗L = ⃗r × p⃗ (particle)
⃗L = I⃗ω (rigid body rotating about axis) IAωA + IB ωB = I′Aω′A + I′Bω′B (primes indicate ‘final’) | Chapter 11: Static Equilibrium Static equilibrium conditions: ⃗Fnet = 0 ⃗τ

FAQs

What topics are included in the NJIT Physics 111 formula sheet?

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.

How does the sheet present motion formulas?

It lists displacement, velocity, and acceleration relationships for constant velocity and constant acceleration cases, including projectile motion and position/velocity vector forms.

What gravitation relationships are provided?

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.

Oct 13, 2026

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