Motion In A Plane Flashcards
What is the difference between a scalar and vector quantity?
Quantities which have direction and magnitude and follow Laws of Vector Addition are called vector quantities.
The quantities which are having magnitude but not direction or even if have direction don’t follow Vectors Law if Addition are called scalar quantities.
How do represent/denote different vector components? What is the relation between them?
Vector A = Ā
Magnitude of Vector A = |Ā| (Mod of Vector A)
Direction of Vector A = Â (A cap)
Relation: Ā = |Ā|•Â
The range for angles between two vectors is?
Range: [0°,180°]
Equilateral ∆ with angle between vector F ____?
60°
Define Vectors:
Equal Vector
Negative Vector
Vectors with equal magnitude and same direction.
Vectors with equal magnitude and opposite direction.
Define Vectors:
Parallel Vector
Anti-Parallel Vectors
Vectors with any magnitude and same direction.
Vectors with any magnitude and opposite direction
Define Vectors:
Co-initial Vectors
Co-planar Vectors
Vectors having same initial points or tails.
Vectors which lie in the same plane.
Define Vectors:
Null Vector
Unit Vector
Vector with zero magnitude and direction not defined.
A vector which has magnitude equal to unit 1 and has fixed direction. |î|=|ĵ|=|k̂|= 1
i cap = unit vector along x-axis
j cap = ,,,, y-axis
k cap = ,,,,, z-axis
How many unit vectors are there in the world?
Minimum rectangular co-ordinate unit vectors required?
∞
3
Define Vectors:
Position Vector
Resolution of Vectors
Vector which represents position of point with respect to origin.
Breaking of vector along axis into it’s components.
What is Triangle Law of Addition?
If two vectors which are to be added kept along adjacent sides of a triangle in such a way that head of one vector coincides with the tail of another vector, the resultant of the two will be shown by a single vector from initial to final.
Resultant vector = R = A +B
(R, A and B are vectors with arrows)
What is the formula for resultant vector’s magnitude?
|R| = √(A^2 + B^2 + 2ABcosQ)
What is the formula for direction (angle) of resultant vector?
α = tan^-1 ((BsinQ)/(A+BcosQ))
Formula for resultant vector when:
Q = 180°
|R| = |A| - |B|
Formula for resultant vector when:
Q = 0°
|R| = |A| + |B|
Formula for resultant vector when:
Q = 90°
|R| = √(A^2 + B^2)
What is Parallelogram Law
When two vectors are kept along two adjacent sides of a parallelogram in such a way that they are co-initial, the resultant of these two vectors is shown by the diagonal of the parallelogram.
You can take a vector anywhere parallely.
What is the general formula of resultant vector for two vectors having same magnitude.
When, |A| = |B| = P
R = 2P•cos(Q/2)
What is the general formula of resultant vector for two vectors having same magnitude.
When, |A| = |B| = P
R = 2P•cos(Q/2)
What is the general formula of resultant vector for two vectors having same magnitude.
When:
Q = 0°
Q = 60°
Q = 180°
R = 2P
R = P√3
R = 0
What is the general formula of resultant vector for two vectors having same magnitude.
When:
Q = 0°
Q = 60°
Q = 180°
R = 2P
R = P√3
R = 0
What is the general formula of resultant vector for two vectors having same magnitude.
When:
Q = 90°
Q = 120°
R = P√2
R = P
What’s the visual location of resultant vector when:
|A| = |B| (Vectors’ magnitude are same)
|A| ≠ |B| (Vectors’ magnitude isn’t same)
Resultant will be inbetween of both vectors.
Resultant will incline towards the bigger vector. Angle formed with the bigger vector will be smaller.
What is the formula for max. and min. resultant vector?
R(max) = |A| + |B|
R(min) = |A| - |B|
|A| - |B| ≤ |R| ≤ |A| +|B|
What do you do when you are only given i, j and k co-ordinates and no info about vector’s angle?
You simply add i, j and k.
If a vector Ā = (p)i + (q)j + (r)k.
What are the X, Y and Z components respectively?
X component = p
Y component = q
Z component = r
If a vector Ā = (13)i + (q)j + (69)k.
And, vector Ē = (m)i - (q)j - (17)k
What are the X, Y and Z components of Ā + Ē respectively?
X component = 13+m
Y component = 0
Z component = 52
What is the Polygon Law of Addition?
When vectors are kept along the sides of a polygon such that head of one vector is coinciding with the tail of another vector, the resultant of these vectors is shown by a simple single vector from initial to final.
How to solve:
Make all vectors co-initial
Resolve all vectors
R(net) = R(x)i + R(y)j
Any closed polygon means Resultant Vector = ?
0
Vector will always incline towards the _____ vector if it’s a _____ Vector.
Larger, Resultant
Vector’s Subtraction is nothing but ____________________??
|A| - |B| = ???
Vector’s addition with opposite direction.
|A| + |-B|
Formula for magnitude of resultant vector of two vectors while subtraction?
|R-| = √(A^2 + B^2 - 2AB•cosQ)
Formula for direction (angle) of resultant vector of two vectors while subtraction?
α’ = tan((BsinQ)/(A-BcosQ))
What is the difference between 1D and 2D motion in respect to equations ??
In 1D motion, no matter what value of time (t), only 1 axis is affected at a time.
Ex: x= f(t)
Ex: y = t^2-3
In 2D motion, two axis vary at the same time.
Ex: x = f(t) AND y = f(t)
Ex: x= t^2-3t and y = t^4+2
2D motion starts when Q between acceleration(vector) and velocity (vector) is not 180° or 0°.
Why and when will 2D motion start?
When Q between acceleration(vector) and velocity (vector) is not 180° or 0°.
Because when Q = 180°,0° particle doesn’t changes axis, it stays in it’s axis only.
