First-year university physics: what the modules cover and how to practise

What first-year physics modules cover

In the US this is often called calculus-based college physics. Other universities may cover the same material in different modules and in a different order, so check your module handbook for the exact syllabus and exam format.

The core topics

• Mechanics with calculus: vector kinematics, Newton's laws, momentum, work and energy.
• Rotation: torque, moment of inertia, angular momentum and rolling.
• Gravitation and oscillations: orbits, simple harmonic motion, damping and waves.
• Electrostatics: Coulomb's law, electric fields and potential, and Gauss's law.
• Circuits: DC circuits and RC charging and discharging.
• Magnetism and induction: magnetic forces and fields, Faraday's law, towards Maxwell's equations.
• Modern physics: special relativity and an introduction to quantum physics.

Worked examples

Mechanics with calculus

A particle has velocity v(t) = 3t² − 4t m s⁻¹. Its acceleration is a = dv/dt = 6t − 4, and its displacement from t = 0 to t = 2 s is:

Zero displacement, even though it moved: it went backwards first, then returned.

Rotational energy

A solid disc of mass 2.0 kg and radius 0.50 m spins at 10 rad s⁻¹. Its moment of inertia is I = ½MR² = 0.25 kg m², so its rotational kinetic energy is ½Iω² = 12.5 J.

Electric field of a point charge

By Gauss's law, the field 0.30 m from a 2.0 μC point charge is E = kq/r² = (8.99 × 10⁹ × 2.0 × 10⁻⁶) ÷ 0.30² ≈ 2.0 × 10⁵ N C⁻¹.

RC discharge

A capacitor charged to 9.0 V discharges through a resistor with RC = 1.0 s. After 2.0 s, V = 9.0e^(−2) ≈ 1.2 V.

Time dilation

A muon with a lifetime of 2.2 μs in its own frame moves at 0.8c. Then γ = 1/√(1 − 0.8²) = 5/3, so in the lab it lives about 2.2 × 5/3 ≈ 3.7 μs.

Work out a photon's energy, a first step into quantum physics, in our Light & Energy course, then press Mark to check your answer in the course:

Use the daily paper as practice

Uni-Sine publishes a free daily University Physics: Year 1 paper. It is a short timed practice paper: 8 questions worth 25 to 35 marks, with a suggested 40 to 55 minutes, marked when you finish. It is not your university's exam, so use it alongside your module's problem sheets and past papers.

• What it covers well: vector kinematics, Newtonian dynamics with calculus, rotational dynamics, gravitation, oscillations and waves, electrostatics and Gauss's law, circuits and RC transients, magnetism and induction, special relativity and introductory quantum physics.
• What it does not cover: lab work and data analysis, thermodynamics, and optics, which some first-year courses include.

Common mistakes in first-year physics

• Treating vectors as numbers. Work in components, or keep track of direction.
• Using the wrong moment of inertia. It depends on the shape and the axis.
• Picking an unhelpful Gaussian surface. Choose one that matches the symmetry of the charge.
• Mixing frames in relativity. Be clear which frame measures the proper time.

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