1. Measurement in Physics AP Physics 1

2. SI units for Physics The SI stands for "System International”. There are 3 fundamental SI units for LENGTH, MASS, and TIME. They basically breakdown like this: SI QuantitySI Unit LengthMeter MassKilogram TimeSecond Of course there are many other units to consider. Many times, however, we express these units with prefixes attached to the front. This will, of course, make the number either larger or smaller. The nice thing about the prefix is that you can write a couple of numbers down and have the unit signify something larger. Example: 1 Kilometer – The unit itself denotes that the number is actually larger than "1" considering fundamental units. The fundamental unit would be 1000 meters

3. Most commonly used prefixes in Physics PrefixFactorSymbol Mega- ( mostly used for radio station frequencies)x 10 6 M Kilo- ( used for just about anything, Europe uses the Kilometer instead of the mile on its roads) x 10 3 K Centi- ( Used significantly to express small distances in optics. This is the unit MOST people in AP forget to convert) x 10 -2 c Milli- ( Used sometimes to express small distances) x 10 -3 m Micro- ( Used mostly in electronics to express the value of a charge or capacitor) x 10 -6  Nano ( Used to express the distance between wave crests when dealing with light and the electromagnetic spectrum) x 10 -9 n Tip: Use your constant sheet when you forget a prefix value

4. Example If a capacitor is labeled 2.5mF(microFarads), how would it be labeled in just Farads? The FARAD is the fundamental unit used when discussed capacitors! 2.5 x 10 -6 F Notice that we just add the factor on the end and use the root unit. The radio station XL106.7 transmits at a frequency of 106.7 x 10 6 Hertz. How would it be written in MHz (MegaHertz)? A HERTZ is the fundamental unit used when discussed radio frequency! 106.7 MHz Notice we simply drop the factor and add the prefix.

5. Dimensional Analysis Suppose we want to convert 65 mph to ft/s or m/s. Dimensional Analysis is simply a technique you can use to convert from one unit to another. The main thing you have to remember is that the GIVEN UNIT MUST CANCEL OUT.

6. Trigonometric Functions Many concepts in physics act at angles or make right triangles. Let’s review common functions.

7. Example A person attempts to measure the height of a building by walking out a distance of 46.0 m from its base and shining a flashlight beam toward its top. He finds that when the beam is elevated at an angle of 39 degrees with respect to the horizontal,as shown, the beam just strikes the top of the building. a) Find the height of the building and b) the distance the flashlight beam has to travel before it strikes the top of the building. What do I know?What do I want? Course of action The angle The adjacent side The opposite side USE TANGENT!

8. Example A truck driver moves up a straight mountain highway, as shown above. Elevation markers at the beginning and ending points of the trip show that he has risen vertically 0.530 km, and the mileage indicator on the truck shows that he has traveled a total distance of 3.00 km during the ascent. Find the angle of incline of the hill. What do I know?What do I want? Course of action The hypotenuse The opposite side The AngleUSE INVERSE SINE!

9. Vectors and Scalars AP Physics 1

10. Scalar A SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it. Magnitude – A numerical value with units. Scalar Example Magnitude Speed20 m/s Distance10 m Age15 years Heat1000 calories

11. Vector A VECTOR is ANY quantity in physics that has BOTH MAGNITUDE and DIRECTION. VectorMagnitude & Direction Velocity20 m/s, N Acceleration10 m/s/s, E Force5 N, West Vectors are typically illustrated by drawing an ARROW above the symbol. The arrow is used to convey direction and magnitude.

12. Applications of Vectors VECTOR ADDITION – If 2 similar vectors point in the SAME direction, add them. Example: A man walks 54.5 meters east, then another 30 meters east. Calculate his displacement relative to where he started? 54.5 m, E30 m, E + 84.5 m, E Notice that the SIZE of the arrow conveys MAGNITUDE and the way it was drawn conveys DIRECTION.

13. Applications of Vectors VECTOR SUBTRACTION - If 2 vectors are going in opposite directions, you SUBTRACT. Example: A man walks 54.5 meters east, then 30 meters west. Calculate his displacement relative to where he started? 54.5 m, E 30 m, W - 24.5 m, E

14. Non-Collinear Vectors When 2 vectors are perpendicular, you must use the Pythagorean theorem. 95 km,E 55 km, N Start Finish A man walks 95 km, East then 55 km, north. Calculate his RESULTANT DISPLACEMENT. The hypotenuse in Physics is called the RESULTANT. The LEGS of the triangle are called the COMPONENTS Horizontal Component Vertical Component

15. BUT……what about the direction? In the previous example, DISPLACEMENT was asked for and since it is a VECTOR we should include a DIRECTION on our final answer. NOTE: When drawing a right triangle that conveys some type of motion, you MUST draw your components tip to tail. N S E W N of E E of N S of W W of S N of W W of N S of E E of S N of E

16. BUT…..what about the VALUE of the angle??? Just putting North of East on the answer is NOT specific enough for the direction. We MUST find the VALUE of the angle. N of E 55 km, N 95 km,E To find the value of the angle we use a Trig function called TANGENT.  109.8 km So the COMPLETE final answer is : 109.8 km, 30 degrees North of East

17. What if you are missing a component? Suppose a person walked 65 m, 25 degrees East of North. What were his horizontal and vertical components? 65 m 25 H.C. = ? V.C = ? The goal: ALWAYS MAKE A RIGHT TRIANGLE! To solve for components, we often use the trig functions since and cosine.

18. Example A bear, searching for food wanders 35 meters east then 20 meters north. Frustrated, he wanders another 12 meters west then 6 meters south. Calculate the bear's displacement. 35 m, E 20 m, N 12 m, W 6 m, S - = 23 m, E -= 14 m, N 23 m, E 14 m, N The Final Answer: 26.93 m, 31.3 degrees NORTH or EAST R 

19. Example A boat moves with a velocity of 15 m/s, N in a river which flows with a velocity of 8.0 m/s, west. Calculate the boat's resultant velocity with respect to due north. 15 m/s, N 8.0 m/s, W RvRv  The Final Answer : 17 m/s, @ 28.1 degrees West of North

20. Example A plane moves with a velocity of 63.5 m/s at 32 degrees South of East. Calculate the plane's horizontal and vertical velocity components. 63.5 m/s 32 H.C. =? V.C. = ?

21. Example A storm system moves 5000 km due east, then shifts course at 40 degrees North of East for 1500 km. Calculate the storm's resultant displacement. 5000 km, E 40 1500 km H.C. V.C. 5000 km + 1149.1 km = 6149.1 km 6149.1 km 964.2 km R  The Final Answer: 6224.14 km @ 8.91 degrees, North of East

22. Adding Vectors by Components 1. Draw a diagram; add the vectors graphically 2. choose x and y axes 3. Resolve each vector into x and y components 4. Calculate each component using sine and cosine 5. Add the components in each direction 6. To find the length of and direction use Pythagorean Theorem and tangent.

23. Example An airplane trip involves three legs, with two stopovers. The first leg is due east for 620km, the second leg is southeast for 440km, and the third leg is at 53° south of west for 550km. What is the plane’s total displacement?