Motion in a plane formula

Motion in a plane involves the movement of an object in two dimensions—usually along the x-axis and y-axis. Here are some important formulas related to motion in a plane:

1. Chapter-4
Motion in a plane
Formulae
1.
UNIT VECTORˆ
A
A
A


2
.Triangle and Parallelogram law of vector addition.
We will find its magnitude
??????= �
??????
+�
??????
+?????? ��?????????????????? ??????
And direction ??????=�??????�
−1
� sin??????
�+�cos??????
3.Resolution of Vector
In two dimension
Vector A is resolved into two components along x and y axis
�= �
�
2
+�
�
2

and direction ??????=�??????�
−1
��
��
In three dimension
Vector A is resolved into two components along x , y and axis
�=
�
�
2
+�
�
2
+�
�
2
4. Dot Product or scalar product
5.Cross or Vector product
6. Instantaneous velocity $OOULJKWFRS\UHVHUYHG1RSDUWRIWKHPDWHULDOFDQEHSURGXFHGZLWKRXWSULRUSHUPLVVLRQ

2. 7.
Instantaneous acceleration

8.
Expression for velocity in a plane


9.
Relative velocity in two dimensions

a.velocity of object A relative to that of B is :

b.velocity of object B relative to that of A is :


10.
Projectile Motion

An object is being thrown with certain velocity or projected is called a
projectile. Such a projectile might be a football, a cricket ball, a baseball or
an
y other object.

 When a body is projected in horizontal direction

Trajectory �=
??????
2�
2
�
2

(Parabolic path)

Time of flight ??????=
2ℎ
??????


Horizontal Range ??????=�
2ℎ
??????

 When a body is projected at an angle ??????
with horizontal direction

Trajectory �=�tan?????? −
??????
2�
2
??????��
2
??????
�
2

(Parabolic path)

Time of flight ??????=
2� �??????�??????
??????


Horizontal Range ??????=
�
2
�??????�2??????
??????


Maximum Height H=
�
2
�??????�
2
??????
2??????

11.
Uniform Circular Motion
When an object follows a circular path at a constant speed, the motion of the object is
called uniform circular motion. The word “uniform “refers to the speed, which is
uniform (constant) throughout the motion.
a = v
2
/R = ω
2
r
ac
= 4π
2
ν
2
r All right copy reserved. No part of the material can be produced without prior permission

3. Thus, the acceleration of an object moving with speed v in a circle of radius r has a
magnitude v
2
/R and is always directed towards the centre. This is why this
acceleration is called centripetal acceleration.

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