KINEMATICS. is a branch of dynamics which describes the motion of objects without consideration of the circumstances leading to the motion . FRAME OF REFERENCE.
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is a branch of dynamics which describes the motion of objects without consideration of the circumstances leading to the motion
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(Ex) 5 meters
50 kilometers per hour (kph)
time, distance, speed, temperature, mass, energy
A quantity that requires both magnitude and direction.
(Ex) 5 meters north (5 m N)
35 km NNE
65 newtons to the left (65 N left)
13 m/s down
velocity, displacement, force, momentum,
electric and magnetic fields
22.5 o W of N
67.5 o N of W
Vectors are usually named with capital
letters with arrows above the letter.
They are represented graphically as arrows.
The length of the arrow corresponds
to the magnitude of the vector.
The direction the arrow points
is the vector direction.
A = 20 m/s at 35° N of E
B = 120 m at 60° S of E
C = 5.8 m west
The secret of how Roman engineers were able to construct “straight as an arrow” roads is a piece of rope with 11 knots folded into three sections with the following ratio: 3:4:5.
Resolving a Vector Into Components
The horizontal, or
x-component, of A is
found by Ax = A cos q.
The vertical, or
y-component, of A is found by Ay = A sin q.
By the Pythagorean Theorem, Ax2 + Ay2 = A2.
Every vector can be resolved using these
formulas, such that A is the magnitude of A, and
q is the angle the vector makes with the x-axis.
Each component must have the proper “sign”
according to the quadrant the vector terminates in.
Analytical Method of Vector Addition
1.Find the x- and y-components of each vector.
Ax = A cos q =
Ay = A sin q =
By = B sin q =
Bx = B cos q =
Cx = C cos q =
Cy = C sin q =
2. Add the x-components.
This is the x-component (Rx) of the resultant.
3. Add the y-components.
This is the y-component (Ry) of the resultant.
4. Use the Pythagorean Theorem to find the
magnitude of the resultant vector.
Rx2 + Ry2 = R2
5. Find the reference angle by taking the inverse
tangent of the absolute value of the y-component
divided by the x-component.
q = Tan-1Ry/Rx
6. Use the “signs” of Rx and Ry to determine the
Θ = tan-1 opp = tan -1 11 = 45 o