Game Development Game Physics Syllabus

Game Physics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Game Physics in Game Development, not a summary of it.

1. 1

   Fundamentals of Physics

   5 topics

   • Newton's Laws of Motion
   • Kinematics
   • Dynamics
   • Work, Energy, and Power
   • Conservation Laws
2. 2

   Mathematics for Physics

   5 topics

   • Vectors and Scalars
   • Differential Calculus
   • Integral Calculus
   • Linear Algebra
   • Numerical Methods
3. 3

   Rigid Body Dynamics

   4 topics

   • Rigid Body Motion
   • Rotation and Angular Momentum
   • Collisions
   • Constraints and Joints
4. 4

   Particle Systems

   4 topics

   • Particle Kinematics
   • Forces and Motion
   • Particle Collisions
   • Springs and Damping
5. 5

   Collision Detection

   4 topics

   • Bounding Volumes
   • Broad Phase Collision Detection
   • Narrow Phase Collision Detection
   • Collision Response
6. 6

   Soft Body Dynamics

   4 topics

   • Mass-Spring Systems
   • Finite Element Method
   • Cloth Simulation
   • Deformable Objects
7. 7

   Fluid Dynamics

   4 topics

   • Navier-Stokes Equations
   • Smoothed Particle Hydrodynamics (SPH)
   • Eulerian Methods
   • Vortex Methods
8. 8

   Physics Engines

   3 topics

   • Overview of Popular Physics Engines
   • Integration with Game Engines
   • Custom Physics Engine Development
9. 9

   Optimization Techniques

   4 topics

   • Spatial Partitioning
   • Level of Detail (LOD)
   • Parallel Computing
   • Performance Profiling
10. 10

    Advanced chapters

    4 topics

    • Inverse Kinematics
    • Ragdoll Physics
    • Destruction Physics
    • Procedural Animation

Game Physics flashcards for Game Development

19 of 51 cards from the Game Physics deck — real questions with worked answers.

1. State Newton's First Law of Motion.

   An object remains at rest or in uniform motion in a straight line unless acted upon by a net external force. This is the law of inertia: if $\sum \vec{F} = 0$, then $\vec{v}$ is constant.

2. State Newton's Second Law and give its vector formula.

   The net force on a body equals its mass times its acceleration: $$\sum \vec{F} = m\vec{a}$$ Equivalently, force equals the rate of change of momentum: $\vec{F} = \frac{d\vec{p}}{dt}$.

3. State Newton's Third Law of Motion.

   For every action there is an equal and opposite reaction: if body A exerts force $\vec{F}_{AB}$ on body B, then B exerts $\vec{F}_{BA} = -\vec{F}_{AB}$ on A.

4. How is linear momentum defined, and how does it relate to force?

   Momentum is $\vec{p} = m\vec{v}$. Newton's second law in momentum form is $\vec{F} = \frac{d\vec{p}}{dt}$, so force is the time rate of change of momentum.

5. What is the difference between a scalar and a vector?

   A scalar has only magnitude (e.g. mass, speed, temperature). A vector has both magnitude and direction (e.g. velocity, force, acceleration), written as $\vec{v}$.

6. Give the four kinematic equations for constant acceleration in 1D.

   $$v = v_0 + at,\quad x = x_0 + v_0 t + \tfrac{1}{2}at^{2}$$ $$v^{2} = v_0^{2} + 2a(x - x_0),\quad x = x_0 + \tfrac{1}{2}(v_0 + v)t$$

7. Define instantaneous velocity and instantaneous acceleration in terms of derivatives.

   Velocity is the derivative of position: $\vec{v} = \frac{d\vec{r}}{dt}$. Acceleration is the derivative of velocity: $\vec{a} = \frac{d\vec{v}}{dt} = \frac{d^{2}\vec{r}}{dt^{2}}$.

8. For projectile motion under gravity (no drag), what are the horizontal and vertical acceleration components?

   Horizontal: $a_x = 0$ (constant horizontal velocity). Vertical: $a_y = -g$ where $g \approx 9.81\ \text{m/s}^{2}$.

9. What is the range of a projectile launched on flat ground with speed $v_0$ at angle $\theta$?

   $$R = \frac{v_0^{2}\sin(2\theta)}{g}$$ Maximum range occurs at $\theta = 45^{\circ}$.

10. Define kinetic energy and give its formula.

    Kinetic energy is the energy of motion: $$KE = \tfrac{1}{2}mv^{2}$$ measured in joules (J).

11. Define gravitational potential energy near Earth's surface.

    $$PE = mgh$$ where $m$ is mass, $g$ is gravitational acceleration, and $h$ is height above a reference level.

12. State the work-energy theorem.

    The net work done on an object equals its change in kinetic energy: $$W_{net} = \Delta KE = \tfrac{1}{2}mv_f^{2} - \tfrac{1}{2}mv_i^{2}$$

13. How is mechanical work defined for a constant force, including the angle dependence?

    $$W = \vec{F}\cdot\vec{d} = Fd\cos\theta$$ where $\theta$ is the angle between force and displacement. For a varying force: $W = \int \vec{F}\cdot d\vec{r}$.

14. Define power and give its two common formulas.

    Power is the rate of doing work: $$P = \frac{dW}{dt}$$ For a force acting on a moving body: $P = \vec{F}\cdot\vec{v}$. Units: watts (W).

15. State the law of conservation of energy for a closed system.

    Total energy cannot be created or destroyed, only transformed. For mechanical systems without dissipation: $KE_i + PE_i = KE_f + PE_f$, i.e. $E$ is constant.

16. State the law of conservation of linear momentum.

    If no net external force acts on a system, its total momentum is conserved: $$\sum \vec{p}_i = \sum \vec{p}_f$$

17. State the law of conservation of angular momentum.

    If no net external torque acts, total angular momentum is conserved: $\vec{L}$ is constant. This is why a spinning skater speeds up when pulling in their arms (smaller $I$, larger $\omega$).

18. What is the dot (scalar) product of two vectors, and what does it compute?

    $$\vec{a}\cdot\vec{b} = a_x b_x + a_y b_y + a_z b_z = |\vec{a}||\vec{b}|\cos\theta$$ It yields a scalar and measures how parallel two vectors are (used for projection).

19. What is the cross (vector) product, and what does it produce?

    $$\vec{a}\times\vec{b} = |\vec{a}||\vec{b}|\sin\theta\,\hat{n}$$ It yields a vector perpendicular to both inputs (direction by right-hand rule), with magnitude equal to the parallelogram area. Used for torque and surface normals.

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