Motion in a Plane Flashcards
Position and Displacemnet Vectors
Used to describe the position of an object in space
Displacement vector
When an object is displaced from its position at point P to a new position at point P’(say), then the vector PP’(make sure to make arrow sign above vector) is called the displacement vector of the object.
Displacement vector of an object does not depend on the path followed by the object.
magnitude of dispalcement vector I PP’ I is either less than or equal to the length of the actual path followed by the object between the two points.
Equality of vectors
Two vectros having the same direction and equal magnitude are said to be equal vectors. This is the necessary condition for any two vectors to be equal. If we shift any of these vectors parallel to itself, and make it overlap with the other, the two vectors will completely coincide with each other.
What if a vector is moved parallel to itself
If a vector is moved parallel to itself, it represents a vector equal to itself ,as in ,the same vector. Such vectors which can be freely moved parallel to themselevs are called free vectors. They do not have fixed locations.
what if there are fixed location vectors
in some cases location or the line of application of a vector is important. Such vectors are called localised vectores.
multiplication of vectors by real numbers
When a vector A is multiplied by a real no n the quantity obtained is a vector nA whose magnitude is n times that of the original vector.
InAI = n IAI.
1) If n is positive, then vector nA and vector A have the same direction.
2) If n is negative, then vector nA and vector A have the opposite directions.
3) If n is zero, the magnitude of vector nA is zero. Such a vector is called a null vector and is denoted by 0 with the vector arrow on top. This is on pg 4 of aakash
since the magnitude of a null vector is zero, its direction cannot be specified.
4) If n is a scaler quantity rather than just a pure no, then the dimension of vector nA is the product of dimensions of n and vector A.
what happens if a vector is subtracted from itself?
if a vector is subtracyed from itself, meaning that vector A is added to vectoer -A, the resultant is a zero vector.
vector A +(vector -A) = vector 0 ( Vector 0 has the vector arrow above it)
Physically it implies that if a body goes form one point to another point and again comes back to the initial point in a given interval, then its net displacemnet is zero during that interval.
Properties of Null Vector:
1) Vector A + Vector 0 = Vector A
2) n vector0= vector 0
3) 0 vector A = vector 0
4) I Vector0 I = 0
As a null vectir has zero magnitude, its direction cannot be specified.
resolution of vectors
the process of splitting up a vector into 2 or more vectors is known as the resolution of a vector.
unit vector
a vector having unit magnitude and pointing in a particuklar direction is called a unit vector. It has no unit and dimensions. It is used to specify a direction only. Unit vetors along the cartesian co-ordiantes x,yand z and given respectively as i cap , j cap and k cap,.
mod of i cap= mod of j cap = mod of k cap=1
