Phys1101 - Introductory Physics 1
Phys1101 - Introductory Physics 1
College of Liberal Arts & Sciences

  • Introduction
  • Lecture 01
  • Lecture 02
    • Lecture 2, Part 1: Announcements
    • Lecture 2, Part 2: Units
    • Lecture 2, Part 3: Vector Introduction
    • Lecture 2, Part 4: Adding Vectors Graphically
    • Lecture 2, Part 5: Vector Addition Examples
    • Lecture 2, Part 6: Vector Component Introduction
    • Lecture 2, Part 7: Trigonometry
  • Lecture 03
    • Lecture 3, Part 1: Introduction
    • Lecture 3, Part 2: Where Were We
    • Lecture 3, Part 3: Vector Components in Detail
    • Lecture 3, Part 4: Scalar Component Description
    • Lecture 3, Part 5: Example of Finding Scalar Components
    • Lecture 3, Part 6: Scalar Component Addition
    • Lecture 3, Part 7: Scalar Addition Example
    • Lecture 3, Part 8: Motion Diagrams
  • Lecture 04
    • Lecture 4, Part 1: Introduction
    • Lecture 4, Part 2: Where Were We
    • Lecture 4, Part 3: Location Location Location …
    • Lecture 4, Part 4: How Fast ??? What Direction ???
    • Lecture 4, Part 5: Speeding Up? Slowing Down?
    • Lecture 4, Part 6: What Happens at a Turning Point?
  • Lecture 05
    • Lecture 5, Part 01: Introduction
    • Lecture 5, Part 02: Where Were We
    • Lecture 5, Part 03: Big Picture:  1D Kinematics
    • Lecture 5, Part 04: Kinematic Problem Solving Steps
    • Lecture 5, Part 05: Example 1
    • Lecture 5, Part 06: Example 2
    • Lecture 5, Part 07: Example 3
    • Lecture 5, Part 08: Free Fall
    • Lecture 5, Part 09: Free Fall and Kinematic Equations
    • Lecture 5, Part 10: Example 4
    • Lecture 5, Part 11: Example 5
  • Lecture 06
    • Lecture 6, Part 1: Introduction
    • Lecture 6, Part 2: Where Were We
    • Lecture 6, Part 3: Reading Quiz
    • Lecture 6, Part 4: Graph Basics
    • Lecture 6, Part 5: Practice Makes Perfect…
    • Lecture 6, Part 6: The Tangent Line
  • Lecture 07
    • Lecture 7, Part 1: Introduction
    • Lecture 7, Part 2: Where Were We
    • Lecture 7, Part 3: 2D Motion Diagrams
    • Lecture 7, Part 4: Trajectories
    • Lecture 7, Part 5: Why Work With Components…
    • Lecture 7, Part 6: Key Vectors in 2D
    • Lecture 7, Part 7: Watching 2D Motion
    • Lecture 7, Part 8: Dropping Versus Firing…
  • Lecture 08
    • Lecture 8, Part 1: Introduction
    • Lecture 8, Part 2: Where Were We
    • Lecture 8, Part 3: 2D Kinematic Problems:  The Big Picture
    • Lecture 8, Part 4: 2D Kinematic Problem Solving Steps
    • Lecture 8, Part 5: Example – Part a
    • Lecture 8, Part 6: Example – Part b
    • Lecture 8, Part 7: Your Turn
  • Lecture 09
    • Lecture 9, Part 1: Introduction
    • Lecture 9, Part 2: Where Were We
    • Lecture 9, Part 3: What is Special About Projectile Motion?
    • Lecture 9, Part 4: Example Part a
    • Lecture 9, Part 5: Example Part b
    • Lecture 9, Part 6: Example Part c
    • Lecture 9, Part 7: Your Turn
  • Lecture 10
    • Lecture 10, Part 1: Introduction
    • Lecture 10, Part 2: Where Were We
    • Lecture 10, Part 3: Dynamics:  Why Does Velocity Change?
    • Lecture 10, Part 4: Physical Interpretation of Newton’s Laws
    • Lecture 10, Part 5: What is a Force?
    • Lecture 10, Part 6: Mathematics of Newton’s 2nd Law
  • Lecture 11
    • Lecture 11, Part 1: Introduction
    • Lecture 11, Part 2: Where Were We
    • Lecture 11, Part 3: Free Body Diagram and Vector Nature of Newton’s 2nd Law
    • Lecture 11, Part 4: Common Forces:  Weight
    • Lecture 11, Part 5: Common Forces:  Tension
    • Lecture 11, Part 6: Common Forces:  Normal Force
    • Lecture 11, Part 7: Common Forces:  Friction
    • Lecture 11, Part 8: Problem Solving Steps
    • Lecture 11, Part 9: Example
  • Lecture 12
    • Lecture 12, Part 1: Introduction
    • Lecture 12, Part 2: Where Were We
    • Lecture 12, Part 3: Example 1
    • Lecture 12, Part 4: Example 2
    • Lecture 12, Part 5: Example 3
  • Lecture 13
    • Lecture 13, Part 1: Introduction and Where Were We?
    • Lecture 13, Part 2: Why/When Do We Need Newton’s Third Law?
    • Lecture 13, Part 3: Newton’s 3rd Law
    • Lecture 13, Part 4: Changes To Our Problem-Solving Steps
    • Lecture 13, Part 5: Example 1
    • Lecture 13, Part 6: Ropes and Pulleys
    • Lecture 13, Part 7: Example 2
    • Lecture 13, Part 8: Your Turn
  • Lecture 14
    • Lecture 14, Part 01: Introduction
    • Lecture 14, Part 02: Where Were We ?
    • Lecture 14, Part 03: Uniform Circular Motion:  What You Need To Know
    • Lecture 14, Part 04: Example 1
    • Lecture 14, Part 05: Example 2
    • Lecture 14, Part 06: Example 3
    • Lecture 14, Part 07: Optional Roller Coaster Example
    • Lecture 14, Part 08: Satellite Example
    • Lecture 14, Part 09: The Universal Law of Gravitation
    • Lecture 14, Part 10: Satellite Example Continued
  • Lecture 15
    • Lecture 15, Part 1: Introduction and Where Were We?
    • Lecture 15, Part 2: Energy Conservation:  The Basics
    • Lecture 15, Part 3: How Do You Calculate the Net Work?
    • Lecture 15, Part 4: New Problem Solving Steps
    • Lecture 15, Part 5: Example 1
    • Lecture 15, Part 6: Example 2
    • Lecture 15, Part 7: Last Example
    • Lecture 15, Part 8: Final Quiz Questions…
  • Lecture 16
    • Lecture 16, Part 1: Introduction and Where Were We?
    • Lecture 16, Part 2: Defining Our New “Energy Conservation Starting Equation”
    • Lecture 16, Part 3: Defining Mechanical Energy
    • Lecture 16, Part 4: New Problem Solving Steps
    • Lecture 16, Part 5: First Example
    • Lecture 16, Part 6: Second Example
    • Lecture 16, Part 7: Last Example
    • Lecture 16, Part 8: Redo Example From Last Lecture
  • Lecture 17
    • Lecture 17, Part 1: Lecture
  • Lecture 18
    • Lecture 18, Part 1: Introduction and Where Were We?
    • Lecture 18, Part 2: Momentum Change of a Single Object
    • Lecture 18, Part 3: Conservation of Momentum
  • Lecture 19
    • Lecture 19, Part 1: Introduction and Where Were We?
    • Lecture 19, Part 2: Let’s Start With Another Example
    • Lecture 19, Part 3: Elastic Collisions
    • Lecture 19, Part 4: Remaining Quiz Questions
  • Lecture 20
    • Lecture 20, Part 1: Introduction and Where Were We?
    • Lecture 20, Part 2: Rotational Kinematics:  The Basics
    • Lecture 20, Part 3: Examples
  • Lecture 21
    • Lecture 21, Part 1: Introduction and Where Were We?
    • Lecture 21, Part 2: Describing Motion ALONG the Circular Path…
    • Lecture 21, Part 3: Examples
    • Lecture 21, Part 4: Rolling Motion
  • Lecture 22
    • Lecture 22, Part 1: Introduction and Where Were We?
    • Lecture 22, Part 2: A Net Torque Causes Angular Acceleration
    • Lecture 22, Part 3: Torque Example
    • Lecture 22, Part 4: Equilibrium Example
    • Lecture 22, Part 5: Moment of Inertia
    • Lecture 22, Part 6: Non-Equilibrium Example
    • Lecture 22, Part 7: Another Example
  • Lecture 23
    • Lecture 23, Part 1: Introduction and Where Were We?
    • Lecture 23, Part 2: The Basics of Oscillatory Motion
    • Lecture 23, Part 3: Hooke’s Law
    • Lecture 23, Part 4: Kinematics of Simple Harmonic Motion
    • Lecture 23, Part 5: Example
  • Lecture 24
    • Lecture 24, Part 1: Lecture
  • Lecture 25
    • Lecture 25, Part 1: Introduction
    • Lecture 25, Part 2: The Basics of Wave Motion
    • Lecture 25, Part 3: Motion of a Particle on a Wave
    • Lecture 25, Part 4:  Motion of The Wave Crest
    • Lecture 25, Part 5: Examples
Lecture 07 » Lecture 7, Part 6: Key Vectors in 2D

Lecture 7, Part 6: Key Vectors in 2D

https://youtu.be/Pmz3c6YYhp0

PHYS 1101: Lecture Seven, Part Six

So, here’s a picture to help me summarize for you, the key vectors that we’re going to work with in 2D. To really help define the scope of the typical problem that we’ll have. We’re going to be describing the motion. For example, here’s a car that’s rounding a corner. They’ll be some initial snapshot in time, put a spot here for the car being at this location at time t-0. And then, at the end of our problem, I’m going to put another spot here to indicate at Time t. This is the position of this object whose motion we want to describe.

Here are the key variables that we need, the key vectors. We’re going to want position vectors at the start of the problem, at t-0 and at the end of the problem, at Time t. So, somewhere, we’ve defined an origin. We have to know where 0-0 is. And then, these position vectors describe the coordinates, the x-0, y-0 at the initial time, t-0. The coordinates x, y at the final time, at time-t, the end of the problem.

Between these two times, we may have reason to think about the displacement vector. The displacement vector is the vector difference between r-0 and r. From start to finish, it’s the arrow that points from where we were to where we ended up. That’s Delta r.

And then, we may have need to talk about the average velocity. Velocity, remember, is displacement over time. So, in two dimensions, it becomes this vector Delta r over Delta t. If these two times were just two brief snapshots in a motion diagram, we’re accustomed to drawing between these two spots, a velocity vector. That would be this, an average velocity. It’s the same direction as the displacement between these two points.

We’re going to need, then, the next level, which is the acceleration vector. Is the difference between two velocity vectors divided by time. So, each of these vectors; position, velocity and acceleration, we’re going to have to work with the scalar components of those.

For this one, I have got x knot and y knot. For this vector, I have the scalar components x and y. Here they are, x and y. For velocity, I’m going to have an initial velocity in my problem and a final velocity. Those are going to have x and y components. And then, I’m going to have an acceleration.

So, here’s a good sketch of that. Somewhere, I’ve got my origin. I’ve got the scope of my problem. The motion I’m focused on from start to finish. Start is going to mean at Time t-0, where was the object? And usually, I think I can say, always, we’re going to start the clock then. Motion is going to occur and then, at some later time, t, that object is going to be at this location. With its final coordinates x-y, given that it had some initial coordinates, x-0, y-0.

Again, x-0 is going to mean the literal value compared to the origin of where it’s sitting above the x-axis. And it’s y-0 is going to be where it’s sitting above the y-axis or along the y-axis. And then, the same idea here at the end. What’s the x-y coordinates at this instant?

At the beginning of the problem, I can have an initial velocity. That literally is the speed and the direction that that object is headed right here. I’m going to have to break that vector up into a v-0 y component. And a v-0 x component to describe this motion.

So, a real life hypotenuse, I’m going to work with these two sides of this right triangle. Likewise, at the end of the problem, my final velocity, I’m going to need to work with the x-component and the y-component. Those vectors.

My acceleration may have a y-component and an x. Okay, it’s a lot of variables, now, so if you had a hard time remembering the 7 that we dealt with in Chapter 2, you now are going to be taxed further and have to remember more variables. But hopefully, you understand now, the importance of doing that. You have to know when I show you the variable v-0 x, that that physically has to represent the horizontal part of the initial velocity.

The velocity of that object at t-0. V-y, it has to represent at Time-t, the end of our problem, the vertical component of the total, final velocity vector. Hopefully you get the idea. Memorize those. Make yourself flashcards.

Here, I just have it sketched again for you to emphasize this point. I’m not going to belabor it. But everything I have in blue is going to represent variables that are connected and relate to the vertical part to the motion. I’ve got a y-0, an initial y part to the velocity. A-y, final v-y.

In purple, I’ve got the variables that describe the horizontal part to the motion. X-knot, e-0-x, a-x, etc. These variables, let’s count them. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. 12 of them, now, that you have to memorize and know physically what they mean. It’s time, position and velocity at the start. Time, position, velocity at the end. And the acceleration in-between.

So, here is quiz question for you, number 7. I’ll just let you pause the video here and read it yourself. How many variables do we need now? And let’s include t-0, even though we’re always going to set that equal to 0. How many mathematical variables are we going to have to work with now, to uniquely describe motion in two dimensions?

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