Motion - Motion in a Plane

Scalars and Vectors: Scalar quantities have only magnitude (e.g., distance, speed), while vector quantities have both magnitude and direction (e.g., displacement, velocity, acceleration). Motion in a plane involves two-dimensional vectors.

Definition of Motion in a Plane: It refers to motion in two dimensions, where the position of an object is defined by two coordinates, typically $(x, y)$. Examples include an object moving in a circular path or a projectile.

Uniform Circular Motion: When an object moves in a circular path with a constant speed, its motion is called Uniform Circular Motion. Although the speed is constant, the velocity is variable because the direction of motion changes continuously at every point.

Acceleration in Circular Motion: Since the velocity vector changes direction at every point along the circular path, circular motion is always an accelerated motion. The acceleration is directed towards the center of the circle.

Direction of Velocity: At any point on the circular path, the direction of the velocity vector is along the tangent to the circle at that point.

Centripetal Force: For an object to move in a circle, a force must act upon it towards the center of the path. This center-seeking force is called centripetal force.