AP Physics 1 Review Notes
Unit 1: Kinematics
Vectors vs. Scalars:
Vectors: Magnitude and direction.
Scalars: Magnitude only.
Distance vs. Displacement:
Distance: Total path length (scalar).
Displacement: Straight-line distance between initial and final positions (vector).
Δx = xf - xi
Distance >= |Displacement|.
Average Velocity:
v_{avg} = \frac{Δx}{Δt} (vector).
Average Acceleration:
a_{avg} = \frac{Δv}{Δt} (vector).
Instantaneous Velocity/Acceleration: Value at a specific time.
Uniformly Accelerated Motion (UAM) Equations:
5 variables, 4 equations. Knowing 3 allows you to solve for the other 2.
Graphs:
Position vs. Time: Slope is velocity.
Velocity vs. Time: Slope is acceleration. Area under the curve is change in position.
Acceleration vs. Time: Area under the curve is change in velocity.
Area above the horizontal axis is positive, area below is negative.
Vector Components:
Resolve vectors into x and y components using sine and cosine.
Pay attention to the angle's reference (not always from the horizontal).
Projectile Motion:
Only force is gravity (near Earth's surface).
a_y = -9.81 \frac{m}{s^2} ≈ -10 \frac{m}{s^2}
UAM equations apply in the y-direction.
a_x = 0, constant velocity in the x-direction.
Relative Motion:
Motion description depends on the observer's frame of reference.
Involves vector addition.
Unit 2: Force and Translational Dynamics
Center of Mass:
x{cm} = \frac{\sum{i} mi xi}{\sum{i} mi}
Can replace position with velocity or acceleration.
Forces:
Vectors resulting from interactions between objects.
Free Body Diagrams:
Show all forces acting on an object.
Forces originate from the center of mass.
Offset forces slightly for clarity.
Never break forces into components on a free body diagram.
Force Normal: Perpendicular to the surface, pushing away.
Force of Tension: Parallel to the rope, a pull.
Newton's First Law (Law of Inertia):
Object at rest stays at rest, object in motion stays in motion with constant velocity, unless acted upon by a net external force.
Inertia: Resistance to acceleration.
Newton's Second Law:
\vec{a} = \frac{\vec{F}_{net}}{m}
Translational Equilibrium:
Net force is zero.
Object at rest or moving with constant velocity (acceleration is zero).
Newton's Third Law:
For every force object 1 exerts on object 2, object 2 exerts an equal and opposite force on object 1.
Forces act simultaneously.
Gravitational Force:
F_g = mg
Direction: Towards the center of mass of the planet (down).
Force of Friction:
Parallel to the surface, opposes sliding motion, independent of the applied force's direction.
Kinetic Friction: F{kf} = μk F_N (surfaces sliding).
μ_k: Coefficient of kinetic friction (no units, cannot be negative, experimentally determined).
Static Friction: F{sf} ≤ μs F_N (surfaces not sliding).
μ_s: Coefficient of static friction.
Friction is independent of surface area.
Newton's Law of Universal Gravitation:
Fg = G \frac{m1 m_2}{r^2}
G is the gravitational constant.
Directed along the line connecting the centers of mass, towards the other mass.
Local Gravitational Field:
Little g, nearly constant on the surface.
Found by equating the two gravitational force equations.
Ideal Spring Force (Hooke's Law):
F_s = -kx
k is the spring constant, x is the displacement from equilibrium.
Direction: Towards equilibrium.
Negative sign: Force and displacement are opposite.
Spring constant: Slope of Force vs. Displacement graph.
Tangential Velocity:
Linear velocity of an object moving in a circle.
Perpendicular to radius, parallel to path.
Centripetal Acceleration:
Directed inward, towards the center of the circle.
Caused by the changing direction of tangential velocity.
a_c = \frac{v^2}{r}
Period (T): Time for one complete circle.
Frequency (f): Revolutions per second; T = \frac{1}{f}
Centripetal Force:
Net force in the