>> There's a lot going on in physics, of course. And one of the things that you need to be very comfortable with is this idea of units and unit conversion. So, let's spend just a little time talking about units. Okay, if I give you a number, say 55, that might not mean very much to you. But if I said, "55 miles per hour," now that means a little more to you. So, units are the way of sort of quantifying the numbers that we're talking about. If I said, "55 centimeters per hour," that's a very different meaning to you than something like 55 miles per hour. So, in physics we use the international standard of units, SI units. Those are, of course, the kilogram, the meter and the second. And these units that you've heard of, but are maybe not totally familiar with and one reason you might not be so familiar with them is in the United States we use the English system of units. All right, so, let's talk about conversion, because we just mentioned 55 miles per hour, 55 miles per hour is, of course, a speed. How do we convert that -- -- to some other units? Well, it's very simple. All you have to do is multiply by 1. Okay, let's multiply by 1 every time. And let's ask the following question, let's say we have a person running. And they're running at 20 meters per second. How fast is that in miles per hour? And before we do that, let's ask this question, is this reasonable? Should they be able to run at 20 meters per second? Okay, so let's convert 20 meters per second to miles per hour. And what we said is all we have to do is multiply by 1 every time. So, what do we remember about, say, centimeters to inches? That's one thing that maybe we remember. And what remember is that 1 inch is 2.54 centimeters. This stuff here in parentheses is the number 1. 1 inch over 2.54 centimeters, that's the number 1, it's just in these funky units. All right, but that doesn't quite get us where we need, because we have to get centimeters out of there. So we remember that there's 100 centimeters per meter. Okay. Then what are we left with? Well, we can cross out the meters, we can cross out the centimeters and now we're left with inches and somehow we got to get inches into miles. So, we remember that there are 12 inches in 1 foot. And maybe you remember there 5280 feet in a mile. So, inches, crosses out with inches. Feet crosses out with feet. And we're left with miles. So, we've got 20 times 100 divided by 2.54 times 12 times 5280. We are in miles per second. All right, that's good. Now we got to get rid of seconds. So, 60 seconds in a minute, 60 minutes in an hour. Okay, every time you multiply by 1 you can take this number and flip it the other way. Which one do you put on top and which one do you put on bottom? It's to cancel out the units appropriately. Okay, so any time you have something in the denominator you can cross out the corresponding units in the numerator. Minutes in the denominator crosses out with minutes in the numerator and now we're left with hours. And we have some numbers to multiply here. We got 20 times 100, times 60, times 60 and we're going to divide by 2.54 times 12 times 5280 and we're going to end up with miles per hour. And now we can multiply this stuff out. So, when you are multiplying out big numbers like this you can always approximate it on paper and I encourage you to do this, because it's good practice. So, 20 is 2 times 10 to the 1. 100 is 10 to the 2. 60 is 6 times 10 to the 1. And we have another 1, 6 times 10 to the 1. And then we are going to divide by 2.54 times 12, which is 1.2. Times 10 to the 1. 5280, which is 5.3 times 10 to the 3. And we should be able to multiply all those numbers and while I'm doing this, maybe you guys can plug it into your calculator and just see what you get. All right, so we got a 2 times a 6, which is 12. And 12 times 6 is -- what's 12 times 6? 72. And then we've got a 10 to the 1. We're going to add another 2 there, another 1 there, another 1 there, so we just count up the zeroes. 1, 2, 3, 4, 5. 72 times 10 to the 5 upstairs. Downstairs what do we have? Well, we've got 2 and a 1/2 times 1.2 times 5.3, that maybe is a little hard to do in your head, but let's just approximate. Let's say this is a 3, this is a 1 and this is a 5. So, that would be 15. And we have a 10 to the 3 down there. Okay. And, so, now we've got 72 over 15 or 72 times 10 to the over a 150 times 10 to the 2. And that is approximately what? Well, that's a little bit less than a half. Right? So, let's say it's around 0.45. And then we have 10 to the 3 and that is 4. We move it over 3 spots, so we get 1, 2, 3 and we should end up with around 45 miles per hour. Did we do that right? >> This we did wrong right here, right? >> Yeah. >> Came out with the right answer, but the sig fig is off. >> What did you guys get when you plugged it in your calculator? >> 44.74. >> 44.74 miles per hour. But this last step here I think we messed something up. >> It should be 15 times 10 to the 4. >> You forgot like the 10 to the 1, you didn't at the bottom. >> You tell me. >> This one, right there? >> Yeah. >> That one right there. So this is actually 10 to the 3. And this 10 to the 2. Good. Now we're good. Everybody agree with that? >> Yeah. >>All right, so, 44 miles per hour. Can you run at 44 miles per hour? No, I mean, that would be like running down the road next to the cars and just cruising along, that's way too fast. So, your intuition was right. 20 meters per second is probably too fast for somebody to run. And the idea is that if you don't know exactly the units you're dealing with, if they make sense or not, those numbers, put them into units that do make sense to you and see. Okay. And let's come up with a way to remember this. 20 went to about 44, so let's approximate this. 1 meter per second is approximately 2 miles per hour. Okay, so if you are running at 20 meters per second it's approximately 40 miles per hour. Okay. Just double it. And this will help you make sense of the answers that you get on your homework problems. [ Music ]
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
1. Intro to Physics Units
Unit Conversions
Video duration:
10mPlay a video:
Related Videos
Related Practice