### Physics

Michael Gathara

Built for simplicity

This site is not meant to be a learning center rather a review site. It assumes you have a surface level knowledge of every subject covered. The goal is not to replace Ap Classroom or teacher based instruction, but rather to supplement it.

Built of off my AP physics class, Khan Academy, various websites, and the AP Physics 1 guided learning plan.

If you can not see the equations clearly please change the math renderer from CHTML to SVG by

• Right click equation
• Hold equation on mobile
• Hover over math settings
• Math Renderer
• SVG

Website built from scratch using:

• Html, Css
• Vanilla JavaScript
• MathJax
• It's also still a work in progress so formatting and design may change as I come up with a better way of presenting information

Legal Stuff

• Desmos may save cookies to enable the use of graphs and by using this site you agree to them
• The underlying domain uses Google Analytics. By using this site you agree to those as well.
• The underlying privacy policy for this site. Which basically says I don't collect anything

Note style inspired by Nav

- Michael Gathara

Version: 0.3.9

# Unit One | Kinematics

### Kinematics:

Deal with pure motion. Usually from the beginning to the end of the described motion. Usually two types, motion with constant Velocity or motion with constant Acceleration

### Vector and Scalar:

Vector

• Has direction
• Has magnitude
• Examples:
• 5 meters/second, North
• 6 miles, East

Scalar

• Only has magnitude
• Examples:
• 5 meters
• 5 degrees celsius

### Displacement and Distance:

Displacement:

• How far away something is from the initial point
• Example:
• An object travels 5 meters north, turns and travels 5 meters east, turns and travels 5 meters north, turns and travels 5 meters west. What is the displacement of the object?
• The object traveled in a square and landed where it started. Thus displacement is zero

Distance

• How much area an object has covered.
• Example:
• An object travels 5 meters north, turns and travels 5 meters east, turns and travels 5 meters north, turns and travels 5 meters west. What is the distance the object has covered?
• The object covered 5+5+5+5 = 20 meters.

### Velocity & Speed

Velocity

• The rate at which a position changes. A vector quantity
• Example:
• A person rapidly moves one step forward and one step back. The resulting velocity is zero since their overall position did not change
$$\Delta Velocity = \frac{\Delta displacement}{\Delta time}$$

Scalar

• The rate of which an object covers a distance within a given Time. A scalar quantity
• $$\Delta Speed = \frac{\Delta Distance}{\Delta Time}$$

### Acceleration

• How quickly something speeds up or slows down
• $$A = \frac{V-V_o}{T} = \frac{\Delta V}{\Delta T}$$

### Linearization

• The process of linearizing a graph
• This site goes over it pretty well. Will add native graphs later
• Linearization Examples

### The Big Four Equations

1. $$V_f^2 = V_i^2 + 2*A*D$$
2. $$D = V_i * T + \frac{1}{2}A * T^2$$
3. $$V_f = V_i + A * T$$
4. $$D = \frac{V_i + V_f}{2} * T$$

Where

• D for Displacement
• A for acceleration
• T for Time
• V for Velocity
• Vf for Final Velocity where Vi is for initial velocity

### Projectile Motion

• Projectile Motion deals with the motion of objects thrown into the air.
• Deals with acceleration and gravity mostly
• Acceleration in the y direction is always -9.81m/s/s unless stated otherwise

Graphs

• Consider the graph
I had a native graph here, but it works nicely on Desktop and not mobile. You can toggle it in developer tools. Mobile optimization for native graphs is not the move right now. So here is Desmos

• Let's assume it is a velocity, time graph
• Seems like the object is moving at an increasing velocity with a constant positive acceleration
• Finding the area underneath the line gives you displacement.
• Find area underneath till a second later. so area of a triangle with a base and height of 1
• $$\frac{1}{2}*b*h = \frac{1}{2}*1*1 = 0.5 meters$$
• You can also do this using the following equation
• $$X = \frac{1}{2}(V+U)T$$
• Where V is final velocity and U is initial velocity. A better way to write it would be
• $$X = \frac{1}{2}(V_f+V_i)T$$
• Plug
• $$X = \frac{1}{2}(1+0)1 = 0.5 meters$$

Now given a position time graph. You can find the slope to get the velocity

• Assume the same graph is used and you want to find velocity in 2 seconds:
• $$M = \frac{rise}{run} = \frac{Y_2-Y_1}{X_2-X_1}$$
• Using the coordinates (0 seconds,0 meters) and (2 seconds,2 meters)
• $$M = \frac{2-0}{2-0} = \frac{2}{2} = 1$$
• We find that the object had a velocity of 1m/s during the 2 second mark
• Which makes sense since the object traveled 2 meters in 2 seconds.
• This also works when the object is in a state of deceleration

Acceleration, Time Graphs

• Whew
• Let's use the graph above as well here. A constantly increasing line for a constantly increasing acceleration
• Since it is increasing by a factor of 1 each second the acceleration is 1 meter/per second/for every second (1m/s/s)(1m/s^2)
• They allow us to find the area underneath the graph in order to get the velocity in the given timeframe.

- Michael Gathara

# Unit Two | Dynamics

### Equilibrium

• Equilibrium is simple. Simply the condition of a system in which something stays constant
• This something can be
• Energy
• Motion
• Examples:
• An object with 60 newtons of gravity pushing down on it while also a 60 newton normal force pushing up on it.
• This object is simply in equilibrium and full equilibrium if no other forces are acting on it
• If all the forces cancel each other out it is known to be in equilibrium

### Newton's First Law

• Also known as the Law of inertia
• Inertia
• Inertia is the resistance of an object to any change in velocity, a change in speed or direction
• First Law
• Simply put. An object in motion tends to stay in motion while an object at rest tends to stay at rest

### Newton's Second Law

• In equation form
• $$F = M*A$$
• Where
• F = Force in Newtons
• M = Mass usually in Kg
• A = Acceleration usually in m/s/s

### Newton's Third Law

• For every action there is an equal and opposite reaction
• Examples:
• When you sit in a chair the chair reacts with an equal reaction. Thus you stay in one spot in the y axis.
• Objects with a net force of zero in the y axis or x axis respectively

### Friction

• Friction is the resistance that two objects encounter on each other
• Described with the equation:
• $$F_f = μ* N$$
• Where:
• F = frictional force
• μ static or μ kinetic being the coeffiecent of friction respectively
• N = normal force
• The coeffiecent of friction is usually given

### Ramps & Inclined Planes

• Normal force is always perpendicular to the surface.
• Gravity is always pointing straight down to the core of the planet
• Force of gravity is usually made up of two components and can be found using the equation:
• $$F_n = M*G*Sin\emptyset$$
• More In-Depth Explaination: Physics Classroom

• ### Free Body Diagrams

• Used to show forces acting on an object
• Can be used to determine if an object is in equilibrium
• The big four forces
• Friction
• Applied
• Gravity
• Normal Force

### Force and Net Force

• Force is the magnitude of any interaction that can change the motion of velocity of an object.
• Usually said by the equation:
• $$F = M * A$$
• Where:
• F = Force in newtons
• M = Mass usually in kg
• A = acceleration usually in m/s/s
• Net Force is the sum of all forces acting on an object.
• Examples:
• An object has an applied force of 5 newtons and a frictional force of 4 newtons.
• The net force would be 1 newton to the applied side.
• Objects in equilibrium have a zero net force.
• Net Force is vector sum of forces.

# Inertial Mass vs Gravitational Mass

• Inertia Equations:
1. Hoop about a symmetric axis
2. $$I = M*R^2$$
3. Solid cylinder
4. $$I = \frac{1}{2}M*R^2$$
5. Solid Sphere
6. $$I= \frac{2}{5}M*R^2$$
8. $$I = \frac{1}{12}M*L^2$$
9. Solid Cylinder, central diameter
10. $$I = \frac{1}{4}M*R^2 + \frac{1}{12}M*L^2$$
12. $$I = \frac{1}{2}M*R^2$$
13. Thin spherical shell
14. $$I = \frac{2}{3}M*R^2$$
16. $$I = \frac{1}{3}M*L^2$$
17. Integral Formula
18. $$I_p = \sum_{i=1}^N *M_i * R_i^2$$

# Notes

### Great Tools

Cool tools I use for the Physics site.

All free

- Michael Gathara