3.2 Physics

Physics Fundamentals

Physics is the fundamental science that studies matter, its motion and behavior through space and time, and the related entities of energy and force. It aims to understand how the universe behaves. The DCAT heavily tests classical mechanics, thermodynamics, optics, and basic electromagnetism.

Motion and Kinematics

Kinematics describes the motion of points, bodies, and systems without considering the forces that cause them. It relies heavily on vectors (having magnitude and direction) and scalars (having only magnitude).

Key kinematic quantities include:

• Displacement ($\Delta x$): A vector representing the change in position from the starting point to the ending point.
• Distance: A scalar representing the total path length traveled.
• Velocity ($v$): The rate of change of displacement ($v = \Delta x / \Delta t$). It is a vector.
• Speed: The rate of change of distance (scalar).
• Acceleration ($a$): The rate of change of velocity over time ($a = \Delta v / \Delta t$). It can refer to speeding up, slowing down (deceleration), or changing direction.

Kinematic equations (for constant acceleration):

1. $v = v_0 + at$
2. $\Delta x = v_0t + \frac{1}{2}at^2$
3. $v^2 = v_0^2 + 2a\Delta x$

Exam Trap: Do not confuse distance (scalar) with displacement (vector). If you run exactly one lap around a 400m track, finishing precisely where you started, your distance is 400m, but your displacement is 0.

Newton's Laws and Forces

Dynamics explains the forces that cause motion. A force is a push or pull resulting from an object's interaction with another object. The SI unit of force is the Newton (N).

Newton's Three Laws of Motion:

1. First Law (Inertia): An object at rest stays at rest, and an object in motion stays in uniform motion with the same speed and direction unless acted upon by a net external force.
2. Second Law ($F=ma$): The acceleration of an object is directly proportional to the net force acting upon it and inversely proportional to its mass.
3. Third Law (Action/Reaction): For every action, there is an equal and opposite reaction. Forces always occur in pairs.

Common forces encountered in physics problems:

• Gravity ($F_g$): The downward force exerted by Earth ($F_g = mg$, where $g \approx 9.8$ m/s$^2$).
• Normal Force ($F_N$): The perpendicular support force exerted by a surface.
• Friction ($F_f$): The force opposing motion between surfaces in contact. Static friction prevents motion, while kinetic friction opposes ongoing motion ($F_f = \mu F_N$).
• Tension ($T$): The pulling force transmitted axially by a string or cable.

Work, Energy, and Power

Work ($W$) is defined as the energy transferred to or from an object via the application of force along a displacement. It is calculated as $W = Fd \cos \theta$, where $\theta$ is the angle between the force and displacement vectors. Work is zero if the force is perpendicular to the motion.

Energy is the capacity to do work, measured in Joules (J). The main forms in classical mechanics are:

• Kinetic Energy (KE): Energy of motion ($KE = \frac{1}{2}mv^2$).
• Gravitational Potential Energy (PE): Stored energy based on an object's height in a gravitational field ($PE = mgh$).
• Elastic Potential Energy: Energy stored in compressed or stretched springs ($PE = \frac{1}{2}kx^2$).

The Law of Conservation of Energy dictates that energy cannot be created or destroyed in an isolated system, only transformed from one form to another. For example, a falling object converts potential energy into kinetic energy.

Power ($P$) is the rate at which work is done or energy is transferred ($P = W/t$). The SI unit is the Watt (W), which equals one Joule per second.

Thermodynamics

Thermodynamics is the study of heat and temperature and their relation to energy and work.

• Zeroth Law: If two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other.
• First Law: Energy conservation. The change in internal energy equals heat added minus work done by the system ($\Delta U = Q - W$).
• Second Law: Entropy of an isolated system always increases over time. Heat flows spontaneously from hot to cold.

Optics: Light, Mirrors, and Lenses

Optics is the branch of physics studying the behavior and properties of light.

• Reflection: Light bouncing off a surface. The angle of incidence always equals the angle of reflection.
• Refraction: The bending of light as it passes from one medium to another with a different index of refraction, governed by Snell's Law ($n_1 \sin \theta_1 = n_2 \sin \theta_2$). Total internal reflection occurs when light attempts to move from a higher to lower index medium at an angle greater than the critical angle.
• Mirrors: Plane mirrors produce virtual, upright, unmagnified images. Concave mirrors converge light and can produce real (inverted) or virtual (upright) images depending on object placement. Convex mirrors diverge light and always produce virtual, upright, reduced images.
• Lenses: Convex lenses converge light (like concave mirrors), while concave lenses diverge light (like convex mirrors).

Electricity and Magnetism

Electricity deals with stationary and moving charges (electrons and protons). Coulomb's Law states that the force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them ($F = k(q_1q_2)/r^2$). Like charges repel; opposite charges attract.

Key circuit concepts:

• Voltage (V): The electric potential difference between two points, providing the "push" for charge (Volts).
• Current (I): The rate of flow of electric charge (Amperes).
• Resistance (R): The opposition to the flow of current, caused by material properties (Ohms).
• Ohm's Law: Relates these three variables: $V = IR$.

Circuits can be wired in series (one path for current) or parallel (multiple paths). In a series circuit, current is constant throughout, and resistances add up. In a parallel circuit, voltage is constant across each branch, and equivalent resistance decreases as more branches are added.

Magnetism is fundamentally produced by moving electric charges. A current-carrying wire generates a magnetic field in circular loops around the wire. Electromagnetism unifies electric and magnetic forces, showing that changing magnetic fields induce electric fields (Faraday's Law of Induction) and changing electric fields induce magnetic fields.