>> Hello class, Professor Anderson here. We're talking about angular momentum today. And let's see what we know about momentum and what we don't know about angular momentum. So we're all familiar with this term of momentum, right? We've talked about how linear momentum, p is just m times v. But what is angular momentum? As you might expect this has to do with rotational motion. So angular momentum we actually write with an L. And L is equal to r cross p. So let's identify what these different terms are. This is our new angular momentum term, and again for some reason we write it with an L because we've run out of other letters, r is some sort of distance. And in fact it is the distance from the axis of rotation to the object. P is the linear momentum of that object. What about this funny looking x thing? This is actually called the cross product. And the cross product is a mathematical tool for figuring out how to combine two vectors and still maintain a vector quantity over on the left hand side. Remember when we talked about the dot product the end result was a scaler, right, two vectors dotted together would give us a scaler. But now the cross product is in fact a vector quantity and that's why the L has a vector on top of it over on the left side. So this is what we need to understand and let's identify first what the cross product is and then how to apply it to various angular momentum problems. Ok what is this cross product that we're talking about? The cross product is the following, let's say I have vector A and it looks like this and I have vector B and it looks like that. And I want to figure out the cross product between these two, not the dot product. The way you figure it out is you put them together, A and B, and then you figure out what the angle is between them and we're going to call that angle phi. Before when we did the dot product we called it theta so in this case we'll call it phi. The cross product A cross B is defined as the following, it's magnitude of A times magnitude of B times the sine of the angle between them, remember when we did the dot product we had cosine and now it's the sine of the angle between them but there's one more thing that's really important here which is cross product is a vector quantity. This that we've written so far is just a magnitude. And so we need to identify a direction. And so for the direction we do an n hat right there. This is of course the magnitude of vector A. This is the magnitude of vector B. This is the angle between them. And this is the resulting direction which we need to figure out from something called the right hand rule. So how do we figure out this direction? The direction n hat we follow what's called the right hand rule, ok? If I have vector A and vector B I can figure out the direction of the cross product if I'm very careful about following the right hand rule. Now this is a little tricky with the learning glass because my right hand is looking like left hand to you. So I in fact have to use my left hand. You'll notice that the ring is on this hand. This is really my left hand even though it looks like my right hand to you guys. The right hand rule is the following. If I have A cross B and that's going to equal some vector C, the way you figure out the direction is the following, A you do your fingers straight, B is you curl your fingers, C is the direction of your thumb. And it's called the right hand rule because you have to do it with your right hand. So let's see if we can figure it out for this simple example that we just talked about. Ok if we just have two vectors, and I'm going to change the order slightly, let's say we have vector A pointing to the right and we have vector B pointing up. What is A cross B? A cross B is going to be magnitude of A, magnitude of B times the sine of the angle between them with a particular direction. But the angle between these two is a right angle and so we get sine of 90 degrees and so we just get AB n hat. Sine of 90 degrees is of course 1. Now how do we figure out the direction for this thing? Ok which way is it going? Well what we said over here was if I do my fingers straight in the direction of A and then I do my fingers curled in the direction of B that should be the direction for C which is given by my thumb. So let's try it. Ok we have vector A going to the right, fingers straight in that direction. And then I want to curl my fingers towards B which would be up. My thumb is now the direction of C, the direction of the cross product, which is of course, according to how we just did it, out of the screen. Ok so try this at home. Sitting there in front of your computer screen, try it. Put your fingers straight in the direction of A, put your curled fingers up towards the direction of B and what you should get is a thumb coming out of the computer screen right towards you. Ok and so this is going to be A, B and the direction is out of the computer screen. Alright let's take a look at that and make sure it works for everybody at home. We're going to move on to the next topic but if you're having trouble with the right hand rule, definitely come see me in office hours. Cheers.
Table of contents
- 0. Math Review31m
- 1. Intro to Physics Units1h 23m
- 2. 1D Motion / Kinematics3h 56m
- Vectors, Scalars, & Displacement13m
- Average Velocity32m
- Intro to Acceleration7m
- Position-Time Graphs & Velocity26m
- Conceptual Problems with Position-Time Graphs22m
- Velocity-Time Graphs & Acceleration5m
- Calculating Displacement from Velocity-Time Graphs15m
- Conceptual Problems with Velocity-Time Graphs10m
- Calculating Change in Velocity from Acceleration-Time Graphs10m
- Graphing Position, Velocity, and Acceleration Graphs11m
- Kinematics Equations37m
- Vertical Motion and Free Fall19m
- Catch/Overtake Problems23m
- 3. Vectors2h 43m
- Review of Vectors vs. Scalars1m
- Introduction to Vectors7m
- Adding Vectors Graphically22m
- Vector Composition & Decomposition11m
- Adding Vectors by Components13m
- Trig Review24m
- Unit Vectors15m
- Introduction to Dot Product (Scalar Product)12m
- Calculating Dot Product Using Components12m
- Intro to Cross Product (Vector Product)23m
- Calculating Cross Product Using Components17m
- 4. 2D Kinematics1h 42m
- 5. Projectile Motion3h 6m
- 6. Intro to Forces (Dynamics)3h 22m
- 7. Friction, Inclines, Systems2h 44m
- 8. Centripetal Forces & Gravitation7h 26m
- Uniform Circular Motion7m
- Period and Frequency in Uniform Circular Motion20m
- Centripetal Forces15m
- Vertical Centripetal Forces10m
- Flat Curves9m
- Banked Curves10m
- Newton's Law of Gravity30m
- Gravitational Forces in 2D25m
- Acceleration Due to Gravity13m
- Satellite Motion: Intro5m
- Satellite Motion: Speed & Period35m
- Geosynchronous Orbits15m
- Overview of Kepler's Laws5m
- Kepler's First Law11m
- Kepler's Third Law16m
- Kepler's Third Law for Elliptical Orbits15m
- Gravitational Potential Energy21m
- Gravitational Potential Energy for Systems of Masses17m
- Escape Velocity21m
- Energy of Circular Orbits23m
- Energy of Elliptical Orbits36m
- Black Holes16m
- Gravitational Force Inside the Earth13m
- Mass Distribution with Calculus45m
- 9. Work & Energy1h 59m
- 10. Conservation of Energy2h 54m
- Intro to Energy Types3m
- Gravitational Potential Energy10m
- Intro to Conservation of Energy32m
- Energy with Non-Conservative Forces20m
- Springs & Elastic Potential Energy19m
- Solving Projectile Motion Using Energy13m
- Motion Along Curved Paths4m
- Rollercoaster Problems13m
- Pendulum Problems13m
- Energy in Connected Objects (Systems)24m
- Force & Potential Energy18m
- 11. Momentum & Impulse3h 40m
- Intro to Momentum11m
- Intro to Impulse14m
- Impulse with Variable Forces12m
- Intro to Conservation of Momentum17m
- Push-Away Problems19m
- Types of Collisions4m
- Completely Inelastic Collisions28m
- Adding Mass to a Moving System8m
- Collisions & Motion (Momentum & Energy)26m
- Ballistic Pendulum14m
- Collisions with Springs13m
- Elastic Collisions24m
- How to Identify the Type of Collision9m
- Intro to Center of Mass15m
- 12. Rotational Kinematics2h 59m
- 13. Rotational Inertia & Energy7h 4m
- More Conservation of Energy Problems54m
- Conservation of Energy in Rolling Motion45m
- Parallel Axis Theorem13m
- Intro to Moment of Inertia28m
- Moment of Inertia via Integration18m
- Moment of Inertia of Systems23m
- Moment of Inertia & Mass Distribution10m
- Intro to Rotational Kinetic Energy16m
- Energy of Rolling Motion18m
- Types of Motion & Energy24m
- Conservation of Energy with Rotation35m
- Torque with Kinematic Equations56m
- Rotational Dynamics with Two Motions50m
- Rotational Dynamics of Rolling Motion27m
- 14. Torque & Rotational Dynamics2h 5m
- 15. Rotational Equilibrium3h 39m
- 16. Angular Momentum3h 6m
- Opening/Closing Arms on Rotating Stool18m
- Conservation of Angular Momentum46m
- Angular Momentum & Newton's Second Law10m
- Intro to Angular Collisions15m
- Jumping Into/Out of Moving Disc23m
- Spinning on String of Variable Length20m
- Angular Collisions with Linear Motion8m
- Intro to Angular Momentum15m
- Angular Momentum of a Point Mass21m
- Angular Momentum of Objects in Linear Motion7m
- 17. Periodic Motion2h 9m
- 18. Waves & Sound3h 40m
- Intro to Waves11m
- Velocity of Transverse Waves21m
- Velocity of Longitudinal Waves11m
- Wave Functions31m
- Phase Constant14m
- Average Power of Waves on Strings10m
- Wave Intensity19m
- Sound Intensity13m
- Wave Interference8m
- Superposition of Wave Functions3m
- Standing Waves30m
- Standing Wave Functions14m
- Standing Sound Waves12m
- Beats8m
- The Doppler Effect7m
- 19. Fluid Mechanics2h 27m
- 20. Heat and Temperature3h 7m
- Temperature16m
- Linear Thermal Expansion14m
- Volume Thermal Expansion14m
- Moles and Avogadro's Number14m
- Specific Heat & Temperature Changes12m
- Latent Heat & Phase Changes16m
- Intro to Calorimetry21m
- Calorimetry with Temperature and Phase Changes15m
- Advanced Calorimetry: Equilibrium Temperature with Phase Changes9m
- Phase Diagrams, Triple Points and Critical Points6m
- Heat Transfer44m
- 21. Kinetic Theory of Ideal Gases1h 50m
- 22. The First Law of Thermodynamics1h 26m
- 23. The Second Law of Thermodynamics3h 11m
- 24. Electric Force & Field; Gauss' Law3h 42m
- 25. Electric Potential1h 51m
- 26. Capacitors & Dielectrics2h 2m
- 27. Resistors & DC Circuits3h 8m
- 28. Magnetic Fields and Forces2h 23m
- 29. Sources of Magnetic Field2h 30m
- Magnetic Field Produced by Moving Charges10m
- Magnetic Field Produced by Straight Currents27m
- Magnetic Force Between Parallel Currents12m
- Magnetic Force Between Two Moving Charges9m
- Magnetic Field Produced by Loops and Solenoids42m
- Toroidal Solenoids aka Toroids12m
- Biot-Savart Law (Calculus)18m
- Ampere's Law (Calculus)17m
- 30. Induction and Inductance3h 37m
- 31. Alternating Current2h 37m
- Alternating Voltages and Currents18m
- RMS Current and Voltage9m
- Phasors20m
- Resistors in AC Circuits9m
- Phasors for Resistors7m
- Capacitors in AC Circuits16m
- Phasors for Capacitors8m
- Inductors in AC Circuits13m
- Phasors for Inductors7m
- Impedance in AC Circuits18m
- Series LRC Circuits11m
- Resonance in Series LRC Circuits10m
- Power in AC Circuits5m
- 32. Electromagnetic Waves2h 14m
- 33. Geometric Optics2h 57m
- 34. Wave Optics1h 15m
- 35. Special Relativity2h 10m
16. Angular Momentum
Intro to Angular Momentum
Video duration:
7mPlay a video:
Related Videos
Related Practice