1 AP Physics Exam 1 Review Chapter 1 - 4

2 Conversion Factors 2 mile/hr = __ m/s

3 Significant Figures (Digits) 1. Nonzero digits are always significant. 2. The final zero is significant when there is a decimal point. 3. Zeros between two other significant digits are always significant. 4. Zeros used solely for spacing the decimal point are not significant. Example:    7 sig. fig’s   3 sig. fig’s

4 Addition and subtraction with Sig. Figs The sum or difference of two measurements is precise to the same number of digits after the decimal point as the one with the least number of digits after the decimal point. Example: = =20.5

5 Multiplication and Division with Sig. Figs The number of significant digits in a product or quotient is the number in the measurement with the least number of significant digits Example: 2.33  5.5 = =13.

6 Position and Displacement  x = x 2 - x 1 = x f – x i Vector – Magnitude: how far – Direction: Negative sign indicates direction only, it has nothing to do with magnitude.

7 Total Distance, d tot When there is no change in direction: When there is change in direction: where d 1 and d 2 are distances of segments in which there is no change in direction.

8 Average Velocity and Speed Standard Unit: m/s Constant velocity:

9 Instantaneous velocity Instantaneous velocity is the average velocity when the time interval becomes very, very small, essentially zero. Instantaneous velocity is the time-derivative of position function.

10 Acceleration Average acceleration Instantaneous acceleration

11 Constant Acceleration Motion a = constant Let initial time t = 0, then at any time t, velocity and position are given by

12 Free-Fall Motion a = g, downward (g = 9.81 m/s 2 )  Up, down or on top of path  Acceleration can be + or -  g always +  g is acceleration due to gravity (It is not gravity.)

13 Adding Vectors: Head-to-Tail Head-to-Tail method: A B A B A+B – Draw vector A – Draw vector B starting from the head of A – The vector drawn from the tail of A to the head of B is the sum of A + B. Example: A + B

14 Vector Components axax ayay a x y   is the angle between the vector and the +x axis. a x and a y are scalars.

15 Vector magnitude and direction  is the angle from the +x axis to the vector. a axax ayay  x y

16 Adding Vectors by Components When adding vectors by components, we add components in a direction separately from other components. 3-D Component form: x y axax ayay bxbx byby a b r rxrx ryry 2-D

17 Dot product: a  b a b  b a is the projection of b onto a. baba a b 

18 Cross Product: c = a  b Magnitude of c is: – Place the vectors a and b so that their tails are at the same point. – Extend your right arm and fingers in the direction of a. – Rotate your hands along your arm so that you can flap your fingers toward b through the smaller angle between a and b. Then – Your outstretched thumb points in the direction of c. A A  B c is a vector, and it has a direction given by the right-hand-rule (RHR):

19 Position is a 3D vector i k j x z y   r

20 3-D Velocity and Acceleration The instantaneous velocity v of a particle is always tangent to the path of the particle.

21 Projectile Motion Breakdown Horizontal: constant velocity Vertical: Constant acceleration (a y = g, downward)  a y = g if downward is defined as +y direction  a y = -g if upward is defined as +y direction

22 Height, Range and Equation of Path  v y = 0  v x = v 0x = v 0 cos  0 Maximum Height is Minimum speed at top, but Horizontal range is Equation of path is

23 Centripetal Acceleration a a a v v v for uniform circular motion at any time.

24 Uniform Circular Motion Period: Frequency:

25 Relative Motion