Motion In A Plane

Question 1

What is the difference between a scalar and vector quantity?

Answer 1

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.

Question 2

How do represent/denote different vector components? What is the relation between them?

Answer 2

Vector A = Ā
Magnitude of Vector A = |Ā| (Mod of Vector A)
Direction of Vector A = Â (A cap)

Relation: Ā = |Ā|•Â

Question 3

The range for angles between two vectors is?

Answer 3

Range: [0°,180°]

Question 4

Equilateral ∆ with angle between vector F ____?

Answer 4

60°

Question 5

Define Vectors:
Equal Vector
Negative Vector

Answer 5

Vectors with equal magnitude and same direction.

Vectors with equal magnitude and opposite direction.

Question 6

Define Vectors:
Parallel Vector
Anti-Parallel Vectors

Answer 6

Vectors with any magnitude and same direction.

Vectors with any magnitude and opposite direction

Question 7

Define Vectors:
Co-initial Vectors
Co-planar Vectors

Answer 7

Vectors having same initial points or tails.

Vectors which lie in the same plane.

Question 8

Define Vectors:
Null Vector
Unit Vector

Answer 8

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

Question 9

How many unit vectors are there in the world?

Minimum rectangular co-ordinate unit vectors required?

Answer 9

∞

3

Question 10

Define Vectors:
Position Vector
Resolution of Vectors

Answer 10

Vector which represents position of point with respect to origin.

Breaking of vector along axis into it’s components.

Question 11

What is Triangle Law of Addition?

Answer 11

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)

Question 12

What is the formula for resultant vector’s magnitude?

Answer 12

|R| = √(A^2 + B^2 + 2ABcosQ)

Question 13

What is the formula for direction (angle) of resultant vector?

Answer 13

α = tan^-1 ((BsinQ)/(A+BcosQ))

Question 14

Formula for resultant vector when:
Q = 180°

Answer 14

|R| = |A| - |B|

Question 15

Formula for resultant vector when:
Q = 0°

Answer 15

|R| = |A| + |B|

Question 16

Formula for resultant vector when:
Q = 90°

Answer 16

|R| = √(A^2 + B^2)

Question 17

What is Parallelogram Law

Answer 17

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.

Question 18

What is the general formula of resultant vector for two vectors having same magnitude.

Answer 18

When, |A| = |B| = P

R = 2P•cos(Q/2)

Question 19

What is the general formula of resultant vector for two vectors having same magnitude.

Answer 19

When, |A| = |B| = P

R = 2P•cos(Q/2)

Question 20

What is the general formula of resultant vector for two vectors having same magnitude.
When:
Q = 0°
Q = 60°
Q = 180°

Answer 20

R = 2P

R = P√3

R = 0

Question 21

What is the general formula of resultant vector for two vectors having same magnitude.
When:
Q = 0°
Q = 60°
Q = 180°

Answer 21

R = 2P

R = P√3

R = 0

Question 22

What is the general formula of resultant vector for two vectors having same magnitude.
When:
Q = 90°
Q = 120°

Answer 22

R = P√2

R = P

Question 23

What’s the visual location of resultant vector when:
|A| = |B| (Vectors’ magnitude are same)
|A| ≠ |B| (Vectors’ magnitude isn’t same)

Answer 23

Resultant will be inbetween of both vectors.

Resultant will incline towards the bigger vector. Angle formed with the bigger vector will be smaller.

Question 24

What is the formula for max. and min. resultant vector?

Answer 24

R(max) = |A| + |B|
R(min) = |A| - |B|

|A| - |B| ≤ |R| ≤ |A| +|B|

Question 25

What do you do when you are only given i, j and k co-ordinates and no info about vector’s angle?

Answer 25

You simply add i, j and k.

Question 26

If a vector Ā = (p)i + (q)j + (r)k.
What are the X, Y and Z components respectively?

Answer 26

X component = p
Y component = q
Z component = r

Question 27

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?

Answer 27

X component = 13+m
Y component = 0
Z component = 52

Question 28

What is the Polygon Law of Addition?

Answer 28

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

Question 29

Any closed polygon means Resultant Vector = ?

Answer 29

0

Question 30

Vector will always incline towards the _____ vector if it’s a _____ Vector.

Answer 30

Larger, Resultant

Question 31

Vector’s Subtraction is nothing but ____________________??
|A| - |B| = ???

Answer 31

Vector’s addition with opposite direction.
|A| + |-B|

Question 32

Formula for magnitude of resultant vector of two vectors while subtraction?

Answer 32

|R-| = √(A^2 + B^2 - 2AB•cosQ)

Question 33

Formula for direction (angle) of resultant vector of two vectors while subtraction?

Answer 33

α’ = tan((BsinQ)/(A-BcosQ))

Question 34

What is the difference between 1D and 2D motion in respect to equations ??

Answer 34

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°.

Question 35

Why and when will 2D motion start?

Answer 35

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.