game-math-and-physics-basics-in-2d

coordinate and vector concepts\ 0:00 Displacementsdistances along x 7:22 Displacementsdistances along y 10:30 Unit vectors along each axis in 2D space 14:17 Relative positions along coordinate axes 18:04 World space vs. object space, part 1 24:19 World space vs. object space, part 2 29:08 Vector components in mathematical form 41:08 Vector components in unity, 2 objects 47:20 Displacements for tilted objects 50:40 Displacements and scenes translations 55:46 Z axis basics with physical model 1:00:53 Effect of rotation on one object 1:07:18 Vectorsvector components under rotations 1:15:43 Vector components in unity, 3 objects 1:23:13 Difference between distance and displacement vector length 1:31:40 0 magnitude displacements vs big distances 1:37:38 Distance at tiny scales 1:46:36 Angle basics in unity 1:56:28 Magnitude and angle of displacement on unit circle 2:06:25 Vectors from unit vectors 2:17:48 Components from angles and length 2:25:32 Unit vectors from math 2:32:47 Vector addition for displacements, graphical rules 2:40:26 Vector addition math 2:49:33 Graphical vector subtraction 2:57:33 Mathematical vector subtraction 3:05:16 Midpoint of a segment 3:10:41 Centroids of point distributions 3:17:33 Weighted average, basic demo 3:19:58 Weighted average, multiple objects, unity 3:29:16 Simulation of coordinate translations, horizontal and vertical line segments 3:34:12 Diagonal translations on coordinates 3:38:18 2D balance point, physical model 3:42:58 Rotations and translations 3:49:23 Constant speed in 2D, line segments 3:55:52 Square roots in more detail 3:58:53 Constant speed, diagonal movements 4:04:37 Constant velocity in 2D, horizontal and vertical 4:12:35 Constant velocity, slanted segments 4:19:16 Speed vs. velocity for line motions 4:24:08 0 velocity 4:26:37 Average concepts 4:33:09 Average speed in 2D, horizonital segments 4:38:21 Average speed, slanted segments 4:43:40 Average velocity in 2D, horizontal segments 4:49:06 Calculations involving speed and velocity 4:53:44 Average velocity for slanted movements 5:00:49 Displacement vector from given velocity 5:03:14 Desired velocity from object to object 5:09:38 Constant acceleration changing speed 5:16:08 Visualizing acceleration 5:23:12 Average acceleration 5:26:44 Constant acceleration changing velocity 5:29:50 Visualize acceleration 5:36:48 Position vector 5:44:16 Final velocity vector 5:47:57 Basic vertical acceleration 5:53:18 Physical introduction to forces 5:58:56 Cancelling horizontalvertical forces 6:04:29 Cancelling slanted forces 6:09:59 Cancelling four forces graphically 6:14:50 Unbalanced forces 6:22:39 Summation notation applied to forces 6:26:39 Finding a missing vector graphically 6:32:40 Finding a missing force mathematically 6:36:30 Finding a force in a given direction 6:41:57 Force equals mass times acceleration 6:49:32 Velocity from force 7:01:09 Position vector from initial position, velocity and acceleration 7:15:16 Projectile motion summary 7:21:03 Projectile motion specific example 7:25:05 Decomposing projectile motion into individual functions 7:29:34 Understanding x(t) 7:35:02 Understanding y(t) Ideas\ 7:42:46 Dot product basics 7:49:57 Scalar projections with dot products 7:55:55 Projecting velocity components with dot products along x and y axes 8:02:14 Projecting velocity components along slanted vectors