PHYS 0174 — Physics for Science and Engineering 1

PHYS 0174 Study Guide

Basic Physics for Science and Engineering 1

Use this guide to connect physical models, diagrams, calculus, and numerical answers. Pitt describes PHYS 0174 as the first physics course for science and engineering, covering mechanics and waves alongside calculus. A published 2026 syllabus also includes gravitation, rotation, fluids, and oscillations. Course scope: Pitt course description (https://www.physicsandastronomy.pitt.edu/content/phys-0174-basic-physics-science-and-engineering-i-0) and published syllabus (https://www.physicsandastronomy.pitt.edu/sites/default/files/syllabi-files-2026/PHYS%200174%20Syllabus.pdf).

These are original study notes and practice examples. Match the order and depth to your instructor's current syllabus. Formulas use ordinary text so they remain editable when pasted into Word, Google Docs, or a notes app. The symbol Δ means final minus initial; a centered dot is a dot product; × between vectors is a cross product.

What to learn first

Measurement and vectors. Convert units, resolve a vector into components, and choose coordinate axes before using an equation. A negative component identifies direction relative to your axes.
Kinematics. Move between position, velocity, and acceleration using slopes and areas. Distinguish a description of motion from its cause.
Forces. Draw a free-body diagram of one object or a clearly defined system. Apply Newton's second law separately along each axis.
Energy. Choose a system boundary and track kinetic energy, potential energy, and transfers. Energy methods often avoid solving for the entire motion.
Momentum. Use impulse for a force acting over time and momentum conservation for isolated-system collisions.
Rotation. Translate linear ideas into angular ones while remembering that rotational inertia depends on mass distribution and axis choice.
Fluids and waves. Connect pressure, flow, restoring forces, and oscillations to the assumptions of each model.

Important vocabulary

Scalar: Quantity with magnitude but no spatial direction, such as mass.
Vector: Quantity with magnitude and direction, such as velocity.
Displacement: Change in position; different from total distance traveled.
Velocity: Rate of change of position.
Acceleration: Rate of change of velocity, including changes in direction.
Inertial reference frame: Frame in which an object with zero net force moves at constant velocity.
Net force: Vector sum of all external forces on the chosen object.
Normal force: Contact force perpendicular to a surface; it is not always equal to weight.
Static friction: Contact force that opposes relative slipping before sliding begins.
Kinetic friction: Friction during relative sliding.
Work: Energy transferred by a force through displacement.
Conservative force: Force whose work depends only on endpoints.
Impulse: Time integral of force; equals momentum change.
Center of mass: Mass-weighted average position of a system.
Torque: Rotational effect of a force about a chosen point or axis.
Moment of inertia: Resistance to angular acceleration about a specified axis.
Angular momentum: Rotational counterpart of linear momentum.
Equilibrium: Zero net force and, for a rigid body in static equilibrium, zero net torque.
Simple harmonic motion: Oscillation with acceleration proportional and opposite to displacement.
Resonance: Large response near a system's natural frequency; damping limits the response.
Wavelength: Spatial distance between repeating points of a wave.
Superposition: Adding overlapping disturbances in a linear system.

Essential formulas and when they apply

Motion and force

v = dx/dt; a = dv/dt = d^{2}x/dt^{2}. Use component equations for vector motion.
Δx = ∫v dt; Δv = ∫a dt. Include limits for a definite change.
v = v_{0} + at; x = x_{0} + v_{0}t + (1/2)at^{2}; v^{2} = v_{0}^{2} + 2aΔx. These require constant acceleration in the chosen direction.
A_{x} = A cosθ; Aᵧ = A sinθ when θ is measured from the positive x axis.
ΣF = ma for constant mass in an inertial frame.
Weight near Earth's surface: Fg = mg; use g ≈ 9.81 m/s^{2} unless instructed otherwise.
|fs| ≤ μsN; |fk| = μkN in the simple dry-friction model. Static friction adjusts up to its maximum.
Centripetal acceleration: ac = v^{2}/r = ω^{2}r. The inward net force supplies this acceleration; “centripetal force” is not an extra force.

Energy and momentum

W = ∫F · dr; constant-force case W = Fd cosθ.
K = (1/2)mv^{2}; Wnet = ΔK.
Ug = mgy near Earth's surface; Us = (1/2)kx^{2} for an ideal spring.
Δ(K + U) = Wother, where Wother includes work by forces not represented in U.
Power P = dW/dt = F · v for the power delivered by a force.
p = mv; J = ∫F dt = Δp.
Σpinitial = Σpfinal when external impulse is negligible.
Universal gravitation: F = GMm/r^{2}; U = −GMm/r with zero potential at infinity.

Rotation, fluids, and waves

ω = dθ/dt; α = dω/dt; v = rω for circular motion about a fixed axis.
τ = r × F; |τ| = rF sinθ. For fixed-axis rigid-body motion, Στaxis = Iaxisα.
I = Σmᵢrᵢ^{2} or ∫r^{2} dm; Krot = (1/2)Iω^{2}.
L = r × p for a particle; Laxis = Iaxisω for a rigid body rotating about a fixed principal axis.
Rolling without slipping: vCM = Rω; total K = (1/2)mvCM^{2} + (1/2)ICMω^{2}.
Pressure p = Fperpendicular/A; hydrostatic difference Δp = ρgΔh.
Buoyant force FB = ρfluid g Vdisplaced.
Incompressible steady flow: A_{1}v_{1} = A_{2}v_{2}.
Bernoulli: p + (1/2)ρv^{2} + ρgy = constant along a streamline for steady, incompressible, negligible-viscosity flow.
Spring oscillator: ω = √(k/m), T = 2π√(m/k), x = A cos(ωt + φ).
Small-angle pendulum: T = 2π√(L/g).
Wave speed vwave = fλ; stretched string vwave = √(Ftension/μ), where μ is mass per length.
String fixed at both ends: fn = n vwave/(2L), n = 1, 2, 3, … .

Units: force N = kg·m/s^{2}; energy J = N·m; power W = J/s; pressure Pa = N/m^{2}; frequency Hz = 1/s. Use radians in calculus and angular-motion formulas.

Worked examples

Example 1 Force and friction

A 4.0 kg box is pulled horizontally with 20 N. The kinetic friction coefficient is 0.20, and vertical acceleration is zero.

N = mg = 39.24 N. Friction is 0.20 × 39.24 = 7.848 N. The horizontal net force is 20 − 7.848 = 12.152 N. Therefore a = 12.152/4.0 ≈ 3.0 m/s^{2} in the pulling direction. A tilted pulling force would change N, so this calculation would need modification.

Example 2 Variable force

A force F_{x} = 3x^{2} N acts along x, with x measured in meters. From x = 0 to 2.0 m, W = ∫{0}^{2}3x^{2} dx = [x^{3}]{0}^{2} = 8.0 J. For a 2.0 kg object initially at rest, (1/2)mv^{2} = 8.0 J gives v = √8 ≈ 2.83 m/s. Multiplying the final force by the full distance would be wrong because the force changes.

Example 3 Spring oscillation

For k = 200 N/m and m = 0.50 kg, ω = √400 = 20 rad/s and T = 2π/20 ≈ 0.314 s. If amplitude A = 0.030 m, maximum speed is Aω = 0.60 m/s. Doubling amplitude doubles maximum speed but does not change the period in this ideal model.

Practice questions and answers

A ball is launched vertically at 14 m/s. Ignore air resistance. Maximum rise? v^{2} = v_{0}^{2} − 2gh gives h ≈ 10 m.
A 2 kg cart at 3 m/s sticks to a stationary 1 kg cart. Final speed? 2 m/s. Momentum is conserved; kinetic energy is not.
A 10 N perpendicular force acts 0.30 m from a pivot. Torque magnitude? 3.0 N·m.
A wave has f = 5 Hz and λ = 0.80 m. Speed? 4.0 m/s.
What happens to a spring period when mass is quadrupled? It doubles.
Can an object have constant speed and nonzero acceleration? Yes; uniform circular motion changes velocity direction.

Mistakes to catch

Applying constant-acceleration equations when acceleration changes.
Conserving mechanical energy when friction transfers energy out of the modeled mechanical system.
Conserving the momentum of a single object during a collision instead of selecting both objects as the system.
Using a moment of inertia about the wrong axis.
Confusing wave speed with the speed of a vibrating particle.