AP Physics 1 Full Review (Unit 1 - Unit 4)

Dot diagram

Marks the position of an object on equal time intervals

Frame of Reference

Point of View from which motion is viewed

Adding perpendicular vectors

Add tip-to-tail

Components of a vector

Force H at angle T

Y component = Hsin(T)

X component = Hcos(T)

Projectile

Objects only under the influence of gravity

Horizontal and vertical motion independent

Describe motion of projectile

Vertical: a=g y=(1/2)gt²

Horizontal: a=0 x=vt

Center of Mass equation

X = (Sum of all (mx)) / (Sum of all m)

Center of Mass definition

Steady as long as center of mass is above base

Center of Mass of a system —> sums

If no external forces, COM of system must remain at rest

Equilibrium

When object is not accelerating and all forces are balanced

Contact vs Field Forces

Direct contact vs exerted at a distance

Free Body Diagram

Axis parallel to objects motion with COM representing the dot

Don’t label force components directly on FBDs

Newton‘s Third Law

All interactions happen in pairs (equal in magnitude, opposite in direction, same in kid)

(Action-Reaction Force Pairs)

Normal Force

Perpendicular to surface

Contact force when two objects touch eachother

Newton‘s First Law

Object will continue its current motion unless acted upon by a force

Newton‘s Second Law

F(net) = ma

With unbalanced force in direction of a

Mod Atwood Machine

2 body problem = two objects connected by a string

Jacob‘s Law of Tensions

There is one value of tension for the entirety of a single rope

Weight

Attraction between two centers of masses

F=mg

Force of gravity between two objects

F(g) = (Gm1m2) / r²

r = distended between two COMs

Strength of gravitational field

g = (Gm) / r²

Factor of Change Method

Plug in 1 for any variable that doesn’t change

Density

Mass/Volume

Equivalence Principle

Because of non-inertial reference frames, they feel like they’re floating (astronauts)

Inertia

How much an object resists acceleration

F=ma —> m is inertial mass

Kinetic Friction

Sliding friction between two objects

Static Friction

Rolling or no sliding interactions. Variable force depending on what’s needed but limited by a maximum

Coefficients for kinetic and static friction

μ_k < μ_s

Coefficients dependent on both the specific surfaces interacting

Friction Formula

|F_f| <= μ |F_N|

F_N = Normal Force

Spring constant

k. Tells us how stiff the spring is

Spring Force formula

F = kx

x = Distance stretched/compressed from equilibrium

Centripetal Acceleration

Any object moving in a circular path, a component of acceleration is directed towards the center

Objects in a circular path with constant speed, F_NET towards the center

Forces perpendicular to motion vs Forces parallel to motion

Forces perpendicular change directions

Forces parallel change speed

Tangential Acceleration

Rate at which speed changes

Directed tangent to the object’s circular path

Net Acceleration in Circular Motion

Vector sum of centripetal acceleration and tangential acceleration

Equation for Net Force in Circular Motion

F_NET = (mv²)/r

r = radius

v = tangential SPEED

Equation for centripetal acceleration

a_c = v²/r

Centripetal acceleration = part directed towards center

v = tangential SPEED

Kepler’s Third Law

T² = ( 4π²r³ / G(m_SUN) )

T = period or year

***Sideline*** The Milky Way’s diameter is 105,000 light years and its mass is around 700 billion times the mass of the sun. The average mass of a star is 2 times the mass of the sun. Using Kepler’s Third Law, we can estimate that the Milky War has around 350 billion stars. While this estimation comes from a while ago, it still holds up to today’s estimated range of stars.

Translational Kinetic Energy

Translational = change in position

Kinetic = motion

Formula for Kinetic Energy

K = (1/2)mv²

Scalar quantity in joules (J)

Defining a System

• Can be a single object or a collection of objects - up to the individual

• Surroundings = anything outside system (environment)

• External interactions = Interactions between the system and the environment

Work

Amount of mechanical energy transferred in or out of a system

(No work = constant mechanical energy)

Not internal energy transformations

Only forces parallel to displacement to work

Work equation

W = F_|| d = Fdcosθ

F_|| = Force parallel to displacement

d = distance force is exerted over

W = Δk

Conservative Forces vs Nonconservative Forces

Conservative = Path-independent (F_g depends on position, not affected by path)

• Field forces must be included in system to include potential energy

Nonconservative = Path-dependent (friction and air resistance)

Area under a Force v Distance graph =

Work

Work-Energy Theorem

Work = (1/2)m (V_f² - V_i²)

(Mass is constant here)

What energy does friction usually result in?

Thermal Energy —> removes heat from system/distributes it

Potential Energy

Stored energy (field forces, chemical energy)

Elastic Potential Energy

Potential energy of an ideal spring - comes from stretching or compressing from rest length at equilibrium

Hooke’s Law

F = kx

k = spring constant with units of N/m

Equation for Elastic Potential Energy (U_s)

U_s = (1/2)(k)(Δx)²

Gravitational Potential Energy

Associated with the position of an object in a gravitational field.

To appear, both object and Earth/planet must be included in system

Equation for Local Gravitational Potential Energy (U_g)

U_g = mgh

g = gravitational field strength

h = height/vertical position

***It’s up to you to decide where GPE = 0 (h = 0). Ground is usually used.

***Large change in h might require different g value for strength, required multiple equations for U_g

Equation for large-scale Gravitational Potential Energy (U_g)

U_g = -(Gm₁m₂)/r

---

U_g is zero when r = infinity

-U_g because we place U_g = 0 where r = infinity.

Khan Academy Explaination:

When dealing with gravitational potential energy over large distances, we typically make a choice for the location of our zero point which may seem counterintuitive. We place the zero point of gravitational potential energy at a distance \[r\] of infinity. This makes all values of the gravitational potential energy negative.

It turns out that it makes sense to do this because as the distance \[r\]becomes large, the gravitational force tends rapidly towards zero. When you are close to a planet you are effectively bound to the planet by gravity and need a lot of energy to escape. Strictly you have escaped only when \[r=\infty\], but because of the inverse square relationship, we can reach an asymptote where gravitational potential energy becomes very close to zero. For a spacecraft leaving earth, this can be said to occur at a height of about \[5\cdot 10^7~\]meters above the surface which is about four times the Earth's diameter. At that height, the acceleration due to gravity has decreased to about 1% of the surface value.

Common Types of Mechanical Energy

• Kinetic Energy

• Gravitational Potential Energy

• Spring Potential Energy

Energy Bar Charts

Representation of amounts of included energy at different points in time of the motion. If system is defined right, total energy of each chart will be equal

Systems with only conservative forces follow law of conservation of energy

Derive an equation that uses _ to define _ (Energy)

Set beginning energy equal to final energy using specified variables

Power

Rate at which work is done/energy changes with units of Watt (W)

Power Equation

P_avg = W/Δt = ΔE/Δt

P = Fv

Linear Momentum equation (p)

p = mv

Vector value

Newton’s First Law relating to Momentum

Change in momentum requires an F_NET or change in mass

Impulse equation (J)

J = FΔt

J = Δp = p_f - p_i

Units of Newton seconds (Ns)

Area under a Force v Time graph =

Impulse

Impulse-Momentum Theorem

F_avgΔt = p_f - p_i

Basically Newton’s Second Law if external force constant

Impulse = change in momentum

Impulse = Force times time

Total momentum is constant if

it’s in an isolated system with no external interactions

Momentum of a two-block system

Represent the momentum of the center of mass of the two objects

Velocity of the center of mass equation (v_cm)

v_cm = Σ(m_iv_i) / Σm_i

V_cm = (Sum of all momentums)_{final or initial} / (sum of all masses)_{final or initial}

Units of momentum (p)

kgm / s