Chapter 4 covers various concepts of motion in a plane, including vector addition, resolution of vectors, and the dot and cross products. It discusses projectile motion, detailing trajectories, time of flight, and horizontal ranges for objects projected at different angles. Additionally, uniform circular motion is explained, emphasizing the concept of centripetal acceleration associated with circular paths.

1. Chapter-4
Motion in a plane
Formulae
1.UNIT VECTOR
ˆ A
A
A


2 .Triangle and Parallelogram law of vector addition.
We will find its magnitude
𝑹 = 𝑨𝟐 + 𝑩𝟐 + 𝟐 𝐀𝐁𝐜𝐨𝐬 𝜽
And direction 𝛼 = 𝑡𝑎𝑛−1 𝐵 sin 𝜃
𝐴+𝐵 cos 𝜃
3. Resolution of Vector
 In two dimension
Vector A is resolved into two components along x and y axis
𝐴 = 𝐴𝑥
2
+ 𝐴𝑦
2
and direction 𝜃 = 𝑡𝑎𝑛−1 𝐴𝑦
𝐴𝑥
 In three dimension
Vector A is resolved into two components along x , y and axis 𝐴 =
𝐴𝑥
2
+ 𝐴𝑦
2
+ 𝐴𝑧
2
4. Dot Product or scalar product
5.Cross or Vector product
6. Instantaneous velocity
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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
any other object.
 When a body is projected in horizontal direction
 Trajectory 𝑦 =
𝑔
2𝑢2
𝑥2
(Parabolic path)
 Time of flight 𝑇 =
2ℎ
𝑔
 Horizontal Range 𝑅 = 𝑢
2ℎ
𝑔
 When a body is projected at an angle 𝜃 with horizontal direction
 Trajectory 𝑦 = 𝑥 tan 𝜃 −
𝑔
2𝑢2𝑐𝑜𝑠2𝜃
𝑥2
(Parabolic path)
 Time of flight 𝑇 =
2𝑢 𝑠𝑖𝑛𝜃
𝑔
 Horizontal Range 𝑅 =
𝑢2𝑠𝑖𝑛2𝜃
𝑔
 Maximum Height H=
𝑢2𝑠𝑖𝑛2𝜃
2𝑔
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 = v2
/R = ω2
r
ac = 4π2
ν2
r
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3. Thus, the acceleration of an object moving with speed v in a circle of radius r has a
magnitude v2
/R and is always directed towards the centre. This is why this
acceleration is called centripetal acceleration.
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