Motion in 2 Dimensions

Understanding Motion in 2 Dimensions

  • Two-dimensional motion occurs when an object moves in more than one direction or along more than one axis.
  • Two-dimensional motion can be analysed using vector quantities such as displacement and velocity.
  • The vector quantities in two dimensions are described by their magnitude (size) and direction.
  • When an object’s motion is along a curved path, it is described as projectile motion.

Vector Quantities

  • A vector is a physical quantity that has both magnitude and direction.
  • Examples of vector quantities include velocity, acceleration, and displacement.
  • Vectors can be represented graphically using arrows, where the length of the arrow shows the magnitude and the direction of the arrow depicts the direction of the vector.

Vector Addition and Resolution

  • Vector addition is the process of combining two or more vectors.
  • The resultant vector is the vector that results from vector addition, it can also be found by drawing a line from the start of the first vector to the end of the last vector.
  • Vector resolution involves breaking a vector down into its component vectors along the x and y axes.

Projectile Motion

  • A projectile is an object moving under the influence of gravity while its horizontal motion remains constant.
  • Horizontal and vertical motions of a projectile are independent of each other.
  • The trajectory of a projectile is parabolic.
  • The maximum height, range, and time of flight of a projectile can be determined using appropriate equations of motion.

Relative Velocity

  • Relative velocity refers to the velocity of one body in relation to another.
  • If two objects are moving in the same direction, their relative velocity is the difference between their velocities.
  • If two objects are moving in opposite directions, their relative velocity is the sum of their individual velocities.

Newton’s Laws of Motion

  • Newton’s first law (law of inertia) states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force.
  • Newton’s second law states that the rate of change of momentum of a body is directly proportional to the force applied and occurs in the direction in which the force is applied.
  • Newton’s third law states that for every action, there is an equal and opposite reaction.

Understanding Problem-Solving in Kinematics

  • Questions about motion in two dimensions are typically solved by breaking the problem into horizontal and vertical components.
  • Each component can be analysed separately using the principles of kinematics; thereafter, the results are combined to give the final answer.
  • Use of diagrams is encouraged to help visualise and solve problems.