Scalars and vectors
* Rectilinear motion is motion that occurs in a straight line.
* Entities that are described completely with the help of a number along with its unit are called scalars
* A number along with the unit that represents the measure of a physical quantity is called its magnitude.
* Mass, distance, temperature and time are scalars.
* Entities that require specification of the line of action or direction in addition to their magnitude to complete their description are called vectors.
* Displacement, velocity, acceleration and force are vectors.
Operations and vectors
* In the graphical method of vector addition, either the triangle Law of addition or Parallelogram Law addition is used.
* In vector addition, the tail of the second vector always coincides with the head of the first vector.
* Vectors obey the Commutative or Associative Law of Addition.
* To subtract two vectors, you must use the concept of addition of vectors after reversing the direction of the second vector.
Addition of vectors by analytical method
* Unit vectors have a magnitude equal to unity and they indicate a particular direction.
* When dealing with planar motion or two dimensional motion. You need to resolve the given vector along two directions, say i and j only.
A= 7i + 3j
B= 5i + 8j
(A + B)=C = 12i +11j
Addition of vectors by analytical method Parallelogram Law
C = \sqrt{A² + B² + 2AB COS⍬ }
tan ⍺ = B sin ⍬/A+B cos ⍬
lsn5: Motion in a plane
Average velocity, v = Displacement/ Time interval
V = lim△t→△ r /△ t
The direction of velocity at any point on the path is tangential to the path at that point and in the same direction as that of motion.
⍺ =△v/△t
lim△t →0 △ v/△ t = dv/dt=⍺
Motion with constant acceleration and relative velocity in two dimensions
* A body can have two independent simultaneous motions in X and Y direction with constant acceleration.
* When subtracting two vectors, to obtain the relative velocity vector, reverse the second vector and the two vectors.
Projectile motion
* A body that is in flight after it is thrown or projected is called a projectile.
* The path forward by a projectile is a parabola.
* The time of flight is the total time during which the projectile is in motion.
Uniform circular motion
* When a body moves in a circular path at a constant speed, it is said to be in uniform
circular motion.
* As the velocity of the body is changing, it has acceleration which is known as centripetal
acceleration.
* Acceleration of a body in uniform circular motion is always directed towards the centre of
the circle.