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The International System of Units

The International System of Units. Three Basic Units (SI). Many SI Derived Units:. 1 Newton = 1 N = 1 kg ∙ m/s 2 1 Watt = 1 W = 1 N ∙ m = 1 kg ∙ m 2 /s 2. Prefixes for SI Units:. 1 kg = 1 × 10 3 grams 1 ps = 1 × 10 -12 seconds. Conversion Factor. Changing Units:. 1 min = 60 s →.

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The International System of Units

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  1. The International System of Units • Three Basic Units (SI) • Many SI Derived Units: 1 Newton = 1 N = 1 kg ∙ m/s2 1 Watt = 1 W = 1 N ∙ m = 1 kg ∙ m2/s2 • Prefixes for SI Units: 1 kg = 1 × 103 grams 1 ps = 1 × 10-12 seconds Conversion Factor • Changing Units: 1 min = 60 s → PHY 2053

  2. distance: meter • 1791: one ten-millionth of a quadrant of the Earth… • - - - • 1889: platinum-iridium bar • - - - • 1983: The meter is the length of the path traveled by light in vacuum during a time interval of 1 / (299,792,458) of a second • (i.e., by definition, c = 299,792,458 m/s) PHY 2053

  3. time: second • Since long ago (Egyptians and Greeks): 1 day = 24 hours • 1 s = (1/24) x (1/60) x (1/60) of the full Earth turn • However, the Earth • rotation • period • varies by • a few ms… • 1967: The second is the duration of 9,192,631,770 periods of the radiation emitted by caesium-133 atom PHY 2053

  4. mass: kilogram • 1799: 10x10x10 cm3 of water • - - - • 1899: platinum-iridium cylinder (d=h=39 mm) 1 u = 1.66053886 × 10-27 kg • atomic mass unit (u): • 12 u = mass of 12C atom • universal, reproducible, • nor requiring an artifact • Density: The density of a • material, r, is the mass per • unit volume: • r = m/V r(water) = 1.00 g/cm3 PHY 2053

  5. 1-d Motion: Position & Displacement • The x-axis: We locate objects by specifying their position along an axis (in this case x-axis). The positive direction of an axis is in the direction of increasing numbers. The opposite is the negative direction. • Displacement: x(t) The change from position x1 to position x2 is called the displacement, Dx. Dx = x2 –x1 The displacement has both a magnitude, |Dx|, and a direction (positive or negative). time t • Graphical Technique: A convenient way to describe the motion of an object is to plot the position x as a function of time t (i.e. x(t)). PHY 2053

  6. 1-d Motion: Average Velocity • Average Velocity The average velocity is defined to be the displacement, Dx, that occurred during a particular interval of time, Dt (i.e. vave = Dx/Dt). • Average Speed The average speed is defined to be the magnitude of total distance covered during a particular interval of time, Dt (i.e. save = (total distance)/Dt). PHY 2053

  7. Average Velocity: Example Problem A train that is initially at the point xi = 3 km at 3:14 pm travels 7 km to the East to the point xE = 10 km. It then reverses direction and travels 36 km to the West to the final point xf = -26 km arriving at 3:56 pm. What is the train’s average velocity (in km/h) for this trip? Note that the displacement Dx is equal to the average velocity times Dt. PHY 2053

  8. Average Speed: Example Problem A train that is initially at the point xi = 3 km at 3:14 pm travels 7 km to the East to the point xE = 10 km. It then reverses direction and travels 36 km to the West to the final point xf = -26 km arriving at 3:56 pm. What is the train’s average speed (in km/h) for this trip? Note that the total distance d is equal to the average speed times Dt. PHY 2053

  9. 1-d Motion: Instantaneous Velocity x x(t+Dt) x(t)  t t+Dt t shrinkDt Dt PHY 2053

  10. 1-d Motion: Instantaneous Velocity x x(t+Dt) x(t) t  t+Dt t shrinkDt Dt PHY 2053

  11. 1-d Motion: Instantaneous Velocity x x(t+Dt) x(t) t  t t+Dt shrinkDt Dt PHY 2053

  12. 1-d Motion: Instantaneous Velocity x x(t+Dt) x(t) t  t t+Dt shrinkDt Dt PHY 2053

  13. 1-d Motion: Instantaneous Velocity x tangent line at t x(t) Instantaneous velocity v(t) is slope of x-t tangent line at t t t The velocity v(t) is the rate of change of x(t) with respect to t at time t. PHY 2053

  14. v v(t) v2 Dv “rise” v1 Dv a 1-d Motion: Acceleration • Acceleration When a particles velocity changes, the particle is said to undergo acceleration (i.e. accelerate). • Average Acceleration The average acceleration is defined to be the change in velocity, Dv, that occurred during a particular interval of time, Dt (i.e. aave = Dv/Dt). • Instantaneous Acceleration v The acceleration a(t) is the rate of change of v(t) with respect to t at time t. v(t) Instantaneous acceleration a(t) is slope of v-t tangent line at t PHY 2053

  15. v v(t) Instantaneous acceleration a(t) is slope of v-t tangent line at t 1-d Motion: Summary • Instantaneous Velocity The velocity v(t) is the rate of change of x(t) with respect to t at time t. • Instantaneous Acceleration The acceleration a(t) is the rate of change of v(t) with respect to t at time t. PHY 2053

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