Phys 2425: Physics with Calculus – Course Syllabus and Topic Overview

Course Overview

This syllabus outlines the weekly topics and key concepts covered in a typical college-level Physics with Calculus course (Phys 2425). The course systematically introduces foundational principles of mechanics, energy, rotation, oscillations, and thermodynamics, integrating calculus-based analysis throughout.

Weekly Topics and Key Concepts

Week 1: Introduction to Physics and Motion

• Course Introduction: Overview of course structure, expectations, and resources.

• Representations of Knowledge and Problem-Solving in Physics: Understanding how to approach and solve physics problems using various representations (graphs, equations, diagrams).

• Introduction to Position, Displacement, Velocity, and Acceleration:

  • Position (x): Location of an object along a coordinate axis.

  • Displacement (\( \Delta x \)): Change in position, \( \Delta x = x_f - x_i \).

  • Velocity (v): Rate of change of position, \( v = \frac{dx}{dt} \).

  • Acceleration (a): Rate of change of velocity, \( a = \frac{dv}{dt} \).

Week 2: Kinematics in One Dimension and Free Fall

• Kinematics in 1D: Analyzing motion along a straight line using calculus.

• Free Fall: Motion under gravity, neglecting air resistance.

  • Key equations:

    • $v = v_0 + at$

    • $x = x_0 + v_0 t + \frac{1}{2} a t^2$

    • $v^2 = v_0^2 + 2a(x - x_0)$

Week 3: Vectors and Kinematics in Two Dimensions

• Vectors: Quantities with both magnitude and direction.

  • Vector addition, subtraction, and components.

  • Unit vectors and coordinate systems.

• Kinematics in 2D: Projectile Motion:

  • Analyzing motion in horizontal and vertical directions independently.

  • Equations for projectile motion:

    • $x(t) = v_{0x} t$

    • $y(t) = v_{0y} t - \frac{1}{2} g t^2$

Week 4: Circular Motion and Newton's Laws

• Circular Motion: Motion along a circular path; centripetal acceleration $a_c = \frac{v^2}{r}$.

• Newton's 1st and 2nd Laws:

  • 1st Law (Inertia): An object remains at rest or in uniform motion unless acted upon by a net force.

  • 2nd Law: $\sum \vec{F} = m \vec{a}$

Week 5: Newton's 3rd Law and Systems of Objects

• Newton's 3rd Law: For every action, there is an equal and opposite reaction.

• Systems of Interacting Objects: Analyzing forces within systems (e.g., connected objects, pulleys).

• Circular Motion Dynamics: Applying Newton's laws to objects in circular motion.

Week 6: Consolidation and Work-Energy Theorem

• Review of Newton's Laws: Consolidation and understanding check.

• Work and the Work-Energy Theorem:

  • Work (W): $W = \int \vec{F} \cdot d\vec{s}$

  • Kinetic Energy (KE): $KE = \frac{1}{2} m v^2$

  • Work-Energy Theorem: $W_{net} = \Delta KE$

Week 7-8: Energy, Power, and Conservation

• Dissipative Forces and Thermal Energy: Effects of friction and non-conservative forces.

• Power: $P = \frac{dW}{dt}$

• Potential Energy (PE): $PE_{gravity} = mgh$

• Energy Conservation: Total mechanical energy is conserved in the absence of non-conservative forces.

• Energy Diagrams: Visualizing potential energy and motion.

Week 9: Impulse and Momentum

• Impulse (J): $J = \int \vec{F} dt$

• Momentum (p): $\vec{p} = m \vec{v}$

• Conservation of Momentum: In the absence of external forces, total momentum is conserved.

• Collisions and Explosions: Elastic and inelastic collisions; conservation laws applied.

Week 10-12: Rotation and Rigid Body Dynamics

• Describing Rotational Motion: Angular position, velocity, and acceleration.

• Moment of Inertia (I): $I = \sum m_i r_i^2$

• Kinetic Energy of Rotation: $KE_{rot} = \frac{1}{2} I \omega^2$

• Torque (\( \tau \)): $\tau = r F \sin \theta$

• Rotational Dynamics: $\sum \tau = I \alpha$

• Conservation of Angular Momentum: $L = I \omega$ is conserved if net external torque is zero.

Week 13: Simple Harmonic Motion (SHM)

• Simple Harmonic Motion: Oscillatory motion described by $x(t) = A \cos(\omega t + \phi)$

• Dynamics of SHM: Restoring force $F = -kx$; angular frequency $\omega = \sqrt{\frac{k}{m}}$

Week 14-15: Thermodynamics

• Ideal Gas Law: $PV = nRT$

• Work in Gas Processes: $W = \int P dV$

• First Law of Thermodynamics: $\Delta U = Q - W$

• Second Law of Thermodynamics: Entropy and direction of heat flow.

• Heat Engines and Refrigerators: Efficiency and limits.

  • Efficiency: $\eta = \frac{W_{out}}{Q_{in}}$

  • Carnot efficiency: $\eta_{Carnot} = 1 - \frac{T_C}{T_H}$

Exams and Assessments

• Quizzes: Regular quizzes to assess understanding of recent topics.

• Midterm Exam: Covers material from the first half of the course.

• Final Exam: Comprehensive assessment at the end of the semester.

Summary Table: Major Topics and Chapters

Week	Main Topics	Key Chapters
1	Introduction, Motion Concepts	Ch 1
2	Kinematics in 1D, Free Fall	Ch 2
3	Vectors, Kinematics in 2D	Ch 3, 4
4-5	Newton's Laws, Circular Motion	Ch 5-8
6-8	Work, Energy, Conservation	Ch 9-10
9	Impulse, Momentum, Collisions	Ch 11
10-12	Rotation, Rigid Body Dynamics	Ch 12
13	Simple Harmonic Motion	Ch 15
14-15	Thermodynamics	Ch 18-21

Additional Info

• This syllabus provides a logical progression through the core topics of calculus-based physics, emphasizing both conceptual understanding and quantitative problem-solving.

• Students are expected to engage with lectures, quizzes, and exams to reinforce learning.

• Some weeks include consolidation and understanding checks to ensure mastery before advancing.