Planar Motion Motion In A Plane
Concepts to Remember  JEE and CBSE Board Exams: Planar Motion  Motion in a Plane:
Vectors (Basic Definitions):

Position Vector: Represents the position of a particle relative to a fixed origin in a coordinate system.

Displacement Vector: Represents the change in position of a particle from its initial position to its final position.

Velocity: Represents the rate of change of displacement of a particle with respect to time.

Acceleration: Represents the rate of change of velocity of a particle with respect to time.
Equations of Motion:

Equations of Motion in Vector Form: Provide the mathematical relations between acceleration, velocity, and displacement of a particle in motion.

Equations of Motion in Scalar Form: Represent the components of acceleration, velocity, and displacement along specific coordinate axes.
Projectile Motion:

Trajectory of a Projectile: The curved path followed by a projectile due to the combined effect of initial velocity and gravitational acceleration.

Equations of Projectile Motion: Describe the motion of a projectile in terms of time of flight, maximum height, and range.
Uniform Circular Motion:

Kinematic Equations of Uniform Circular Motion: Relate angular displacement, angular velocity, linear velocity, and radius of rotation.

Centripetal Acceleration and Force: Explain the acceleration of an object moving in a circular path and the force required to produce this acceleration.
Tangential and Radial Components:

Tangential and Radial Acceleration in Uniform Circular Motion: Describe the components of acceleration in uniform circular motion: tangential acceleration and radial acceleration.

Components of Velocity and Acceleration: Express velocity and acceleration vectors into tangential and radial components.
Relative Motion:

Concept of Relative Motion: Describes the motion of an object relative to another object in motion.

Relative Velocity: Represents the velocity of an object relative to another object in motion.
Work, Energy, and Power:

Concept of Work in 2D: Explains the concept of work done on a particle moving in a plane.

Concept of Power: Represents the rate at which work is done or energy is transferred.
Impulse and Momentum:

Impulse and Momentum in Vector Form: Provides mathematical relations between impulse, momentum, and force in vector form.

Momentum Conservation Principle in 2D: States that the total momentum of a closed system remains constant in the absence of external forces.
Rotation:

Angular Velocity and Displacement: Describe the angular motion of an object, relating angular displacement, angular velocity, and time.

Angular Acceleration: Represents the rate of change of angular velocity with respect to time.

Rotational Kinematics Equations: Relate angular displacement, angular velocity, angular acceleration, and time in rotational motion.

Torque: Describes the force that causes an object to rotate around an axis, considering its moment arm.
Newton’s Laws of Motion:

Newton’s First Law of Motion: States that an object at rest stays at rest, and an object in motion continues in motion with an unchanging velocity unless acted upon by an external force.

Newton’s Second Law of Motion for Rotational Motion: Relates the net torque acting on an object to its angular acceleration.

Newton’s Third Law of Motion for Rotational Motion: States that for every actionreaction pair, the torques produced are equal in magnitude but opposite in direction.
Friction:

Static and Kinetic Friction: Describe the frictional force between two surfaces in contact, either at rest (static friction) or in motion (kinetic friction).

Coefficient of Friction: Quantifies the resistance to motion between two surfaces.
Collision (1D and 2D):

Elastic Collision in 1D: Describes a collision where both momentum and kinetic energy are conserved.

Inelastic Collision in 1D: Describes a collision where only momentum is conserved, and kinetic energy is lost.

Coefficient of Restitution: Measures the degree of elasticity in a collision.

Oblique Collision in 2D: Describes a collision between two particles in two dimensions, considering both normal and tangential components.
Equilibrium of Forces:

Concept of Equilibrium: Describes the state of an object where the net force acting on it is zero.

Conditions of Equilibrium: Provide the criteria for an object to be in equilibrium in various situations.
Moment of Inertia:

Concept of Moment of Inertia: Represents the resistance of an object to angular acceleration, analogous to mass in linear motion.

Calculation of Moment of Inertia for Simple Bodies: Provides formulas to calculate the moment of inertia for simple objects like spheres, cylinders, and rods.
Parallel Axes Theorem:
 Parallel Axis Theorem for Moment of Inertia: Establishes a relation between the moment of inertia about an axis parallel to the axis passing through the center of mass.
Perpendicular Axis Theorem:
 Perpendicular Axis Theorem for Moment of Inertia: Relates the moments of inertia about two mutually perpendicular axes passing through a point.
WorkEnergy Theorem:

Concept of WorkEnergy Theorem: States that the net work done on an object is equal to the change in its kinetic energy.

Application to Motion in a Plane: Demonstrates the use of the workenergy theorem to solve problems involving motion in a plane.
Projectile Motion and Time of Flight:
 Time of Flight and Maximum Height in Projectile Motion: Derives equations to calculate the time of flight and maximum height reached by a projectile.
Centripetal Force and Newton’s Laws:
 Centripetal Force and its Relation to Newton’s Laws: Explains how Newton’s laws govern the motion of an object in circular motion, focusing on the centripetal force.
Rotational Motion and Inertia:
 Inertia in Rotational Motion: Highlights the role of inertia in resisting changes in rotational motion.
Moment of Inertia and Rotational Motion:
 Moment of Inertia and its Role in Rotational Motion: Explains how the moment of inertia affects the angular motion of an object.
Equilibrium and Rotational Motion:
 Equilibrium in Rotational Motion: Discusses the conditions for an object to be in rotational equilibrium.
Applications of Rotational Dynamics:

Simple Pendulum: Analyzes the motion of a simple pendulum using rotational dynamics concepts.

Physical Significance of Moment of Inertia: Explores the practical implications of the moment of inertia in various situations.