Scalars Vs Vectors
Scalars:
Scalars have only magnitude
Scalars change If their magnitude changes
They can be added according to ordinary laws of algebra
Vectors:
Vectors have both magnitude and direction
they change if either their magnitude , direction, or both change
they can only be added using special laws of vector addition.
Position Vector
a vector which gives position of an object with reference to the origin of a co-ordinate system
a position vector provides two informations:
1. the straight line distance of the object from the origin, O
2. the direction of the object with respect to the origin.
Displacement vector
it is that vector which tells how much and in which direction an object has changed its position in a given time interval.
Polar vectors
Vectors which have a starting point or a point of application.
Axial Vectors
Vectors which represent rotational effect and act along the axis of rotation.
zero vectors
a zero vector or null vector is a vector that has zero magnitude and an arbitrary direction.
Triangle Law of Addition
if two vectors can be represented both in magnitude and direction by the two sides of a triangle take in the same order, then their resultant is represented completely, both in magnitude and direction by the third side of the triangle.
Derive Triangle Law of Addition
Parallelogram law of addition
if two vectors can be represented both in magnitude and direction by the two adjacent sides of a parallelogram drawn from a common point, then their resultant is completely represented by the diagonal of the parallelogram drawn from that point.
Derive Parallelogram Law of Addition
Scalar Product
AB cos theta
Vector Product
AB sin theta
projectile
a projectile is the name given to a. body which once thrown into space with some initial velocity, moves thereafter under the influence of gravity alone.
the path followed by a projectile is called its trajectory.
principle of physical independence of motion
In absence of air resistance, the motion of a projectile is considered as the combination of two independent motions:
a. horizontal motion: uniform velocity
b. vertical motion: under influence of gravity
assumptions used in projectile motion
- there is no air resistance on the projectile
- the effect due to curvature of the Earth is negligible
- the effect due to rotation of the Earth is negligible for all points of the trajectory, the acceleration due to gravity is constant both in magnitude and in direction.
Horizontal Projection derivation with
1. time of flight
2. horizontal distance
3. velocity of the object at any instant
4. if velocity makes an angle with the horizontal
Projectile given angular projection derivation with
1. time of flight
2. horizontal distance
3. velocity of the object at any instant
Uniform circular motion
if a particle moves along a constant path with a constant speed then its motion is said otherwise be uniform motion. Uniform circular motion is an accelerated motion. Velocity is always perpendicular to the radius vector.
angular displacement
angle swept out by its radius in the given time interval.
theta=s/t
angular velocity
the time rate of change of angular displacement.
w=theta/t or 2pi/t
time period
the time taken by a particle to complete one revolution along its circular path.
T= 1/v
frequency
the frequency of an object in a circular path is the number of revolutions completed per unit time.
linear velocity
v=rw
centripetal acceleration
the acceleration of an object which is directed alongg the radius towards the centre of a circular path on which the object is travelling is called centripetal acceleration. a=v^2/ r or rw^2
