PHY 131 Theory Pack Comprehensive Review Notes | Complete Solutions, Fall 2026

PHY131H1 Theory Pack
Comprehensive Review Notes



Contents
1 Kinematics 3
1.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Constant Acceleration Equations . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Interpreting Motion Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Free Fall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.5 Projectile Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.6 Relative Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Dynamics: Newton’s Laws 5
2.1 Newton’s Three Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Mass vs. Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Free-Body Diagram: Flat Surface . . . . . . . . . . . . . . . . . . . . . . . . 5
2.4 Applying Newton’s Second Law . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.5 Atwood Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Friction and Forces on Inclines 7
3.1 Types of Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2 Forces on an Inclined Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.3 Forces on a Horizontal Surface . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.4 Rope at an Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.5 Block on Incline with Hanging Mass . . . . . . . . . . . . . . . . . . . . . . . 8

4 Work, Energy, and Power 9
4.1 Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.2 Kinetic Energy and Work-Energy Theorem . . . . . . . . . . . . . . . . . . . 9
4.3 Potential Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.4 Energy Analysis: Box Pushed on Rough Floor . . . . . . . . . . . . . . . . . 9
4.5 Conservation of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4.6 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9




1

,5 Momentum, Impulse, and Collisions 10
5.1 Linear Momentum and Impulse . . . . . . . . . . . . . . . . . . . . . . . . . 10
5.2 Conservation of Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
5.3 Types of Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

6 Rotation and Angular Momentum 11
6.1 Angular Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6.2 Torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6.3 Moment of Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6.4 Newton’s 2nd Law for Rotation . . . . . . . . . . . . . . . . . . . . . . . . . 11
6.5 Static Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
6.6 Angular Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

7 Oscillations (Simple Harmonic Motion) 13
7.1 Definition of SHM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
7.2 Mass-Spring System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
7.3 Simple Pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
7.4 Energy in SHM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

8 Waves and Sound 14
8.1 Wave Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
8.2 Standing Waves on a String . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
8.3 Sound Intensity and the Doppler Effect . . . . . . . . . . . . . . . . . . . . . 14
8.4 Universal Gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

9 Key Formula Summary 16




2

, 1 Kinematics
1.1 Definitions
Position x: location along axis (m). Displacement: ∆x = xf − xi .
Average velocity: v̄ = ∆x/∆t. Instantaneous velocity: v = dx/dt (slope of x-t
graph).
Average acceleration: ā = ∆v/∆t.

1.2 Constant Acceleration Equations
v = v0 + at x = x0 + v0 t + 21 at2
v 2 = v02 + 2a (x − x0 ) x = x0 + 21 (v0 + v) t

1.3 Interpreting Motion Graphs
x
v
slope = v

slope = a
t ∆x
turn
x-t graph t
v-t graph

ˆ x-t: slope = v; object changes direction at turning point (local max/min).

ˆ v-t: slope = a; shaded area under curve = ∆x.

ˆ Constant v ⇒ straight line on x-t; a = 0.

ˆ Constant a ⇒ parabola on x-t; straight line on v-t.

1.4 Free Fall
Near Earth’s surface (ignore air resistance): g = 9.80 m/s2 downward for all objects. An
object thrown upward and one thrown downward with the same initial speed will have the
same speed at any common height below the launch point.

1.5 Projectile Motion
Horizontal and vertical motions are independent:

x = x0 + v0x t, vx = v0x = const, v0x = v0 cos θ

y = y0 + v0y t − 12 gt2 , vy = v0y − gt, v0y = v0 sin θ

3