Motion in a Plane - Important Formulas, Definitions, and Examples | 11th Physics
Chapter 4: Motion in a Plane
formulas Physics, Formulas, Kinematics, Vectors, Scalars, Motion in Two Dimensions, Definitions
Introduction
Motion in a plane involves the study of objects that move in two dimensions, such as projectile motion and circular motion. This chapter explores vector quantities, their components, and their application in understanding motion in a plane.
1. Scalars and Vectors
Definition:
Scalars are quantities that have magnitude only, while vectors have both magnitude and direction.
- Examples of Scalars: mass, time, speed, distance
- Examples of Vectors: velocity, displacement, acceleration, force
2. Vector Addition
Definition:
Vector addition is the process of combining vectors using methods such as the triangle law or the parallelogram law.
Triangle Law of Vector Addition: If two vectors are represented by the two sides of a triangle, the resultant vector is the third side of the triangle taken in the reverse direction.
3. Resolution of Vectors
Definition:
The resolution of vectors is the process of breaking down a vector into its perpendicular components, typically along the x-axis and y-axis.
Formulas for Components of a Vector:
Vx = V cos θVy = V sin θ
Where V is the magnitude of the vector and θ is the angle with the horizontal axis.
4. Projectile Motion
Definition:
Projectile motion refers to the motion of an object that is projected into the air and moves under the influence of gravity.
Key Formulas for Projectile Motion:
- Horizontal Range:
R = (u² sin 2θ) / g - Maximum Height:
H = (u² sin² θ) / (2g) - Time of Flight:
T = (2u sin θ) / g
Where u is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity.
5. Uniform Circular Motion
Definition:
Uniform circular motion occurs when an object moves in a circular path at a constant speed. However, its velocity continuously changes due to the change in direction.
Key Formula: The centripetal acceleration required to keep an object moving in a circular path is:
a = v² / r
Where v is the tangential velocity and r is the radius of the circular path.
6. Relative Velocity
Definition:
Relative velocity is the velocity of one object as observed from another object moving at a different velocity.
Formula for Relative Velocity:
If two objects A and B have velocities vA and vB respectively, then the relative velocity of A with respect to B is:
vAB = vA - vB
7. Important Definitions
- Displacement: The shortest distance between the initial and final position of an object. It is a vector quantity.
- Velocity: The rate of change of displacement with time. It is a vector quantity.
- Acceleration: The rate of change of velocity with time. It is a vector quantity.
- Centripetal Force: The force that keeps an object moving in a circular path and is directed towards the center of the circle.
Comments
Post a Comment