Motion in a Plane Flashcards
what is a scalar quantity
Quantity that has only magnitude. follows normal algebra
temperature, distance, mass
what is a vector quantity
quantity that has both direction and magnitude and follows vector algebra. displacement,
velocity, acceleration and force.
what is position vector
the vector which gives the position of an obj with respect to the origin is called position vector. represented by** r**
what is displacement vector
Displacement vector is that vector which tells how much and in what direction the object has changed its position in a given time interval. represented by Δr
displacement
vector is the straight line joining the initial and
final positions and does not depend on the actual
path undertaken by the object between the two
positions.
what is a unit vector
a unit vector is avector that has a magnitude of 1 and no units. It is intended to describe the direction in a space.
The unit vectors for for x,y and z axes are icap, jcap a,d kcap.
What are equal vectors
Two vectors A and B are said to be equal if they have same magnitude and direction
What are free and localised vectors
If vectors do not have fixed locations then they are called free vectors.
If the vectors have fixed positions ie fixed location or line of application, they are called localised vectors
what will happen when we multiply a vector with a real no
Multiplying a vector A with a positive number λ
gives a vector whose magnitude is changed by
the factor λ but the direction is the same as that
of A
Multiplying a vector A by a negative number
λ gives a vector λA whose direction is opposite
to the direction of A and whose magnitude is
–λ times |A|.
what is triangle law of addition
If2 vectors can represented in magnitude and direction by the two sides of a triangle taken in the same order , the resultant R is represented completely in direction and magnitude when taken in the opposite order
what is parallelogram law of addition
If the two vectors acting simultaneously at a point can represented in magnitude and driection as adjacent sides of a prallelgram, then the resultant R is represented both in magnitude and direction the diagonal of the parallelogram passing through that point
what is a null vector
A vector whose magnitude is ) is called a null vectro.Since the magnitude of a null vector is zero, its
direction cannot be specified.
ex: velocity vector of an obj at rest
i) the sum of any vector and null vector is vector itself
ii) the prouct of a null vector and any integer is the nulll vector
iii) the product of a null vector and a vector is the null vector
what is the resolution 2 vectors
splitting up of a vector into 2 mutually perpendicular vectors whose sum sum is equal to the original vector is called rectangular resolution of a vector
for limting values, what is inst velocity at any tim
the direction of velocity at any point
on the path of an object is tangential to the
path at that point and is in the direction of
motion.
what is the relation between velocity and acceleration
Note that in one dimension, the velocity and
the acceleration of an object are always along
the same straight line (either in the same di-
rection or in the opposite direction). However,
for motion in two or three dimensions, veloc-
ity and acceleration vectors may have any
angle between 0° and 180° between them.
are motionin x and y directions dependent of each other? why or why not?
the motions in x- and y-directions can be treated
independently of each other. That is, motion in
a plane (two-dimensions) can be treated as two
separate simultaneous one-dimensional
motions with constant acceleration along two
perpendicular directions. This is an important
result and is useful in analysing motion of objects
in two dimensions. A similar result holds for three
dimensions.
