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Today • Announcements: – HW#1 is due Wednesday by 8:00 am – The first extra credit assignment is on the LONCAPA system. The due date is 16-Sept. • Review • Time Travel • Units • Motion • Scalars, Vectors, Tensors ISP209f5 Lecture 2 -1- Review • The speed of light is a constant, independent of the speed of the source. – this is one of the two postulates of Special Relativity (Einstein) – One of the implications is that moving clocks run slow. • Position – location relative to an origin • Velocity – rate of change of position • Acceleration – rate of change of velocity ISP209f5 Lecture 2 -2- Time Travel • Moving at high speed is a way to travel into the future. No problem here; this is correct. • Twin Paradox (stated in class)– resolved by general relativity • The speed of light is fast, but distances in space are large. – We see the Sun as it was 8 minutes ago – We see nearby stars as they were 4-10 years ago – The distance light travels in one year is called a light-year. – We see the nearby Andromeda Galaxy as it was 3 My ago – Looking out at the stars is like looking back in time. • Can we move backward in time? Maybe ISP209f5 Lecture 2 -3- Units • Physical quantities always have a unit attached; for example 2 meters • Some quantities are a combination of units; for example 1 liter = 1000 cm3 (LONCAPA 1000 cm^3 or 1.0E3 cm^3 or 1.0E-3 m^3) • How many liters are in a gallon? • What is the density of materials: density = mass/volume ISP209f5 Lecture 2 -4- Unit Conversions 3.7854l 1.000 gallons 1.000 3.7854l gallon Let's take an example. Suppose we have 16.4 gallons. How many liters is that? 16.4 g 16.4 gal 3.7854l 62.1l gal ISP209f5 Lecture 2 -5- Another example of unit conversion 100 cm m 1.000 100 cm m 2 11.2 cm2 11.2 cm2 1.000 m 1.12103 m2 100 cm ISP209f5 Lecture 2 -6- Prefixes prefix name value n nano 10-9 m micro 10-6 Example: m milli 10-3 c centi 10-2 2.0My 2.0106 y d deci 10-1 2.0My Gy 2My 2103Gy 1000My 1 k kilo 103 M Mega 106 G giga 109 ISP209f5 Lecture 2 -7- LONCAPA Units • We will use the SI system of units. Link • Common units – Kilogram (mass) kg – Meter (length) m – Seconds (time) s – Newtons (force) N – Joules (energy) J – same as N*m/s • The LONCAPA system has help • Frequency is 1/s (Hz) ISP209f5 Lecture 2 -8- Motion Motion of a car as a function of time. 0.6 miles min miles 0.5 1.5 1.25 0.4 1 0.3 0.75 Distance 0.2 0.5 0.1 0.25 Vel 0 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 time min Time min What is the average velocity at 2.5 s? x f xi 0.75miles 0.25miles miles 60 min miles v 0.56 33.6 t f ti 2.7 min 1.8 min min h h We get 0.60 miles/min = 36 mph from the velocity graph. ISP209f5 Lecture 2 -9- Motion Problem 1.5 miles 1.25 E 1 B D 0.75 Distance 0.5 C 0.25 0 A 0 1 2 3 4 5 6 7 Time min ISP209f5 Lecture 2 -10- Scalars, Vectors, Tensors • Physical quantities can have characteristics. • Scalars – a quantity without direction – such as the mass of a object – the magnitude of a vector • Vectors – a quantity that has a length and direction • Tensors – generalized versions of vectors in more than one direction – The number of dimension in a tensor is called the rank – Rank 0 tensor is a scalar – Rank 1 tensor is a vector ISP209f5 Lecture 2 -11- Examples of Scalars • Mass, charge • Speed (magnitude of velocity) • Amount of money in my wallet • The volume of a container (gallons or liters) ISP209f5 Lecture 2 -12- Examples of Vectors • Position – 2 miles East of Spartan Stadium • Velocity – 60 mph toward Detroit • Acceleration – 9.8 m/s^2 down • Note: velocity and acceleration can have opposite directions. Example: a ball moving upward. ISP209f5 Lecture 2 -13- Vectors • Representation 1 meter East • Addition A+B ISP209f5 Lecture 2 -14- Vector Addition and Subtraction Addition Subtraction ISP209f5 Lecture 2 -15- An example of a Tensor • Curvature of space-time: Riemann curvature tensor Rm One number is not sufficient to describe each point in space. ISP209f5 Lecture 2 -16- Time-lines ISP209f5 Lecture 2 -17- Time-Lines and World Diagrams • A world diagram is a plot of time vs. position. • Nothing can go faster than the speed of light, hence all events must fall within a “light cone” • The path of an object is called the world line • Usually the time axis in given in units where a particle moving at c will fall along a 45 degree line, e.g., y vs. ly . ISP209f5 Lecture 2 -18-

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