Introductory Physics course

1. 1.Kinematics

   Kinematics describes motion without asking what causes it. Position, displacement, velocity and acceleration are the core quantities. Displacement and velocity are vectors, so direction matters: walking 5 m east and then 5 m west covers 10 m of distance but zero displacement.

   • $v = v_0 + at$; $\Delta x = v_0 t + \frac{1}{2}at^2$; $v^2 = v_0^2 + 2a\Delta x$; $\Delta x = \frac{v_0 + v}{2}t$.
   • Pick a positive direction and keep signs consistent.
   • On a position-time graph slope is velocity; on a velocity-time graph slope is acceleration and area is displacement.
   Quick check: A ball is dropped from rest. How fast is it falling after 2 s (use $g = 9.8$)?

   $19.6$ m/s

   Includes a worked example, 3 common mistakes and 3 practice questions with answers. Study kinematics

2. 2.Forces and Newton's Laws

   A force is a push or pull, measured in newtons. Newton's first law says an object keeps its velocity unless a net force acts on it. The second law, $F_{\text{net}} = ma$, says the net force sets the acceleration. The third law says forces come in equal and opposite pairs acting on different objects.

   • Weight $W = mg$, with $g \approx 9.8$ m/s².
   • Kinetic friction $f = \mu_k N$; static friction can be anything up to $\mu_s N$.
   • On an incline, split weight into $mg\sin\theta$ along the slope and $mg\cos\theta$ into it.
   Quick check: What net force gives a 1200 kg car an acceleration of 2.5 m/s²?

   $3000$ N

   Includes a worked example, 3 common mistakes and 3 practice questions with answers. Study forces and newton's laws

3. 3.Work and Energy

   Work is done when a force moves an object: $W = Fd\cos\theta$, where $\theta$ is the angle between force and displacement. Energy is the capacity to do work. Kinetic energy $\frac{1}{2}mv^2$ belongs to moving objects; gravitational potential energy $mgh$ depends on height.

   • Units: joules, $1\text{ J} = 1\text{ N} \cdot \text{m}$.
   • Forces perpendicular to motion, like the normal force on a level floor, do no work.
   • Conservation: $\frac{1}{2}mv_1^2 + mgh_1 = \frac{1}{2}mv_2^2 + mgh_2$ when friction is negligible.
   Quick check: Find the kinetic energy of a 3 kg object at 4 m/s.

   $24$ J

   Includes a worked example, 3 common mistakes and 3 practice questions with answers. Study work and energy

4. 4.Momentum

   Momentum is mass times velocity, $p = mv$, a vector measured in kg·m/s. A heavy truck and a fast bullet can have similar momenta. A force applied over time changes momentum; this impulse $J = F\Delta t = \Delta p$ explains why airbags and crumple zones reduce injuries by stretching out the collision time.

   • Conservation: $m_1 v_1 + m_2 v_2 = m_1 v_1' + m_2 v_2'$.
   • Choose a positive direction; velocities in the other direction are negative.
   • Perfectly inelastic: $(m_1 + m_2)v' = m_1 v_1 + m_2 v_2$.
   Quick check: Find the momentum of a 0.15 kg ball at 40 m/s.

   $6$ kg·m/s

   Includes a worked example, 3 common mistakes and 3 practice questions with answers. Study momentum

These topics belong to the course outline. Full explainers for them have not been written yet, so they are summarised here rather than given pages of their own.

DC Circuits

Ohm's law, series and parallel resistors, power.

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