Position & Displacement

Kinematics is the study of motion through describing and relating the position (r→), velocity (v→), and acceleration (a→) of a system. Average Quantities involves taking snapshots in time of an initial and final state of a system and finding the average of the above quantities.

• Lecture 1 | Position & Displacement

Average Velocity & Acceleration

Kinematics is the study of motion through describing and relating the position (r→), velocity (v→), and acceleration (a→) of a system. Average Quantities involves taking snapshots in time of an initial and final state of a system and finding the average of the above quantities.

• Lecture 2 | Average Velocity & Acceleration

In the graphical analysis module, we wish to develop the concepts and tools necessary to interpret and analyze graphs containing information about position, velocity, acceleration, as a function of time. The graphs we will analyze all contain information about the motion of an object.

• Lecture 1 | Graphical Analysis

1D Kinematics of Constant Acceleration

Kinematics is the study of the motion of objects. One dimensional (1-D) kinematics studies the motion of objects moving along a straight line with constant acceleration. The major goal is to develop the ability to mathematically model the motion by applying the kinematic equations for constant acceleration.

• Lecture 1 | 1D Kinematics of Constant Acceleration

1D Kinematics Problem Solving Strategies

This lecture will focus on how to solve the problems introduced in the previous lecture. Today will be an opportunity to flex problem-solving muscles: a major reason for taking physics and a skill to apply to any field of study. Ask questions and make as many mistakes as possible, as this is as low-stakes as it gets (compared to homework, exams, and your future job).

• Lecture 2 | 1d Kinematics Problem Solving Strategies

2D Kinematics

Similar to the previous section, 1D kinematics, this section quantifies the movement of objects. This time it will take into account movement in more than one dimension, for example a car driving in a parking lot or an astronaut in outer space.

• Lecture 1 | 2D Kinematics

Projectile Motion

Projectiles are objects launched with both horizontal and vertical components to their velocity. This section takes what was learned in 2D kinematics and helps quantify this movement. Some examples would be a baseball being thrown or a stuntman in a car driving off a cliff.

• Lecture 2 | Projectile Motion

Newton's Laws 1

Forces Introduction

In this section, we will explore some consequences of Newton's first law, which can be stated as, "an object moving with a constant velocity will continue to move with the same speed and in same direction unless an interaction with another object(s) produces a net external force".

• Lecture 1 | Forces Introduction

FBD & Newton's 2nd Law

Newton's Second Law describes a force as proportional to acceleration, where the mass is the constant of proportionality. Free body diagrams are a method of visualizing and solving force problems.

• Lecture 2 | FBD & Newton's 2nd Law

Application of Newton's 2nd Law

Here's a demonstration and explanation of Newton's Second Law in space.

• Lecture 3 | Application of Newton's 2nd Law

Newton's Laws 2

Friction

Friction arises when two surfaces are in contact with each other and are pushed in a way that makes the surfaces want to slide relative to each other. Note they don't have to be sliding. Air resistance is also a form of friction.

• Lecture 1 | Friction

Inclined Planes

Often times an object we are trying to analyze with FBDs sits atop a surface that is not parallel to the ground. This slight variation adds some noteworthy complexities that we will cover in this section.

• Lecture 2 | Inclined Planes

Newton's Laws 3

Coupled Systems & Pulleys

It is possible for objects to share similar motions with other objects, an example would be a car and the driver, both are traveling at the same speed and direction. When scenarios like this occur, we call it a coupled system. This section will help develop the necessary tools to identify coupled systems and the resulting constraints that arise from this coupling.

• Lecture 1 | Coupled Systems & Pulleys

Forces & Uniform Circular Motion

Objects traveling in a circle at a constant speed are considered to be in uniform circular motion (UCM). Recall velocity has both magnitude and direction, so even though the magnitude of the tangential velocity remains the same in UCM, the direction is constantly changing. For this special case of motion the acceleration points towards the center of the circle which means the net force does as well.

• Lecture 2 | Forces & Uniform Circular Motion

Impulse & Momentum Theorum

Momentum is equal to the mass multiplied by the velocity: p⃗ =mv⃗ . The SI units for momentum are kilogram meters per second (kg*m/s). Momentum can be used to determine both the direction and speed of colliding objects.

• Lecture 1 | Impulse & Momentum Theorum

1D Conservation of Momentum

If the impulse on a system is approximately zero, which occurs if the net force is very small or the duration of the force is very small, then the change in momentum is also approximately zero. That means that if you vectorially add up all the momentum in your system initially, it will equal the net momentum of the system finally. Mathematically this can be written as $\sum{\vec{p}_i} = \sum{\vec{p}_f}$. Applying momentum conservation when applicable will allow you to determine the motion of systems before and after collisions and other interesting scenarios.

• Lecture 1 | 1D Conservation of Momentum

2D Conservation of Momentum

Conservation of Momentum in 2 dimensions follows the same fundamental equations and principles as in 1 dimension. The main difference is that you must use a component analysis and conserve momentum in in both x and y directions.

• Lecture 2 | 2D Conservation of Momentum

Work & Kinetic Energy Theorem

Objects can possess energy in many forms but this section is only going to consider the energy from the translational motion of the system. This motional energy is called kinetic energy (K=12mv2) and notice it is a scalar quantity. It is true that velocity is a vector quantity but when you square it, all direction is lost.

• Lecture 1 | Work & Kinetic Energy Theorem

Potential Energy & Conservation of Energy

When finding the work done by various types of forces, an interesting result arises from the work done by gravity and elastic springs. The work done by both types of forces only depends on the initial and final positions of the object. This means that we can skip the process of calculating work for gravity and springs, and instead write a function that results in the same value that we would have got if we did calculate the work the traditional way.

• Lecture 1 | Potential Energy & Conservation of Energy

Conservation of Energy Application

Check out the OpenStax trailer to learn about the interplay between kinetic and potential energy.

• Lecture 2 | Conservation of Energy Application

Systems & Energy, Collisions

What are the similarities and differences between these two dropped eggs?

• Lecture 3 | Systems & Energy, Collisions

Angular Position, Velocity, & Acceleration for Non-uniform Circular Motion

This section will cover the kinematics (motion) of objects undergoing non-Uniform Circular Motion (nUCM). Objects in UCM travel in a circle but potentially change their speed. Examples include a spinning disk, a loop-the-loop on a roller coaster, a race car speeding out of a semi-circular corner, or children on a merry-go-round that slowing down. Much like linear kinematics, rotational kinematics uses position, velocity, and acceleration to describe the motion.

• Lecture 1 | Angular Position, Velocity, & Acceleration for Non-uniform Circular Motion

Connecting Rotational & Translational Kinematics

What is a Radian? This video helps you visualize the concept.

• Lecture 2 | Connecting Rotational & Translational Kinematics

Torque & the 2nd Law for Rotation

We have previously studied Newton's laws of motion while only considering what happens to the center-of-mass (COM) of an object, otherwise known as a point particle model. In statics and dynamics, we still work under the framework of Newton's laws of motion, but we extend our consideration from the point particle model to also include the shape and size of the object.

• Lecture 1 | Torque & the 2nd Law for Rotation

Application of 2nd Law: Static Equilibrium & Stability

Applying Newton's 2nd law for rotation requires understanding how to calculate torques. Then you add those up and set them equal to the moment of inertia multiplied by the angular acceleration. If an object is in rotational equilibrium, the net torque must add up to zero, resulting in zero angular acceleration.

• Lecture 2 | Application of 2nd Law: Static Equilibrium & Stability

Dynamics & Moment of Inertia

Check out this trailer video from OpenStax about the Moment of Inertia.

• Lecture 3 | Dynamics & Moment of Inertia

Angular Momentum & Rotational Energy

Angular momentum helps us think about how difficult it would be to stop something from spinning if the rotational speed of the object and it's distribution of mass around the axis of rotation was varied. Stopping a merry-go-round is much harder when its full of children. Angular momentum is often used when talking about extended masses, such wheels rotating about an axle or ice skaters spinning faster and faster.

• Lecture 1 | Angular Momentum & Rotational Energy