Unit 1: Kinematics + Intro
How to count significant figures:
Embedded 0’s count (i.e. 101 has 3 sig figs)
Any numbers that aren’t zeros count (i.e. 5263 has 4 sig figs) 0’s after the decimal place count (i.e. 1.00 has 3 sig figs) Trailing 0’s (i.e. 2000 has 4 sig figs)
Numbers after the first nonzero (i.e. 0.0002102 has 4 sig figs) How to add and subtract numbers with proper sig figs:
The result will have the least amount of numbers after the decimal place. (i.e. 1.23 + 1.3 + 10.004 = 12.5)
How to multiply and divide numbers with proper sig figs:
The result will have the least number of sig figs
(i.e. 3.0 x 12.60 = 38)
Metric Conversions
The following is a neat way to ensure success in moving decimals 963 2 1 0 1 2 36912
G M k h da d c m µ n p Big 5
v22=v12+2a∆d ∆d=v1∆t+ 12a∆t2 v2= v1+ a∆tv2= v1+ a∆t ∆d=0.5v2+v1∆t ∆d= v2∆t12a∆t2 ∆d=0.5v2+v1∆t ∆d=v1∆t+ 12a∆t2 ∆d= v2∆t12a∆t2 ∆d = Area under a velocitytime graph a = Slope of a velocitytime graph v = slope of a distancetime graph
[Position, Time] Graphs and their [Velocity, Time] and [Acceleration, Time] equivalents A
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Vector Addition (tip to tail)
Vector = both magnitude and direction Scalar = only magnitude, no direction Ex. Time = scalar, displacement = vector
Graphical Vector Addition  Adding two vectors A and B graphically can be visualized like two successive walks, with the vector sum being the vector distance from the beginning to the end point. Representing the vectors by arrows drawn to scale, the beginning of vector B is placed at the end of vector A. The vector sum R can be drawn as the vector from the beginning to the end point.The process can be done mathematically by finding the components of A and B, combining to form the components of R, and then converting to polar form.

Example of Vector Components Finding the components of vectors for vector addition involves forming a right triangle from each vector and using the standard triangle trigonometry.The vector sum can be found by combining these components and converting to polar form.

Polar Form Example  After finding the components for the vectors A and B, and combining them to find the components of the resultant vector R, the result can be put in polar form bySome caution should be exercised in evaluating the angle with a calculator because of ambiguities in the arctangent on calculators.

Combining Vector Components  After finding the components for the vectors A and B, these components may be just simply added to find the components of the resultant vector R.The components fully specify the resultant of the vector addition, but it is often desirable to put the resultant in polar form.

Air Navigation Problems (Tail to tail)
This sort of problem is when you have one full vector and 2 partial vectors. Steps:
1 Draw the full vector
2 Pick the partial vector of which you know the direction. Draw it tail to tail (or tip to tip) with the full vector 3 Draw the other partial vector TIP to TAIL
River Crossing Problems (Tip to Tail)
This sort of problem is when you have 2 full vectors and you are missing a partial vector. Steps:
1 Draw both full vectors
2 Use the vector component, Pythagorean theorem method
Vector Acceleraton
To determine vector acceleration we must use vector subtraction first to solve for v2  v1 first as in a= v2v1t Now...