Circular motion

Circular Motion Basics

  • Traditionally, motion is described along a straight line (rectilinear motion), but some objects like the moon, earth, and artificial satellites move in a circular path.
  • This unique behaviour is known as circular motion which happens when an object moves in a circle at a constant speed.
  • The velocity is always tangent to the circle at that point of motion.
  • Despite a constant speed, the object moving in a circle does change its velocity as there is a change in direction at every point in the orbit.

Key Terms in Circular Motion

Centripetal Force:
  • Centripetal force is the net force causing circular motion, acting towards the centre of the circle.
  • This force causes an object to move in a circular path and its absence causes the object to move off in a straight line.
  • The word ‘centripetal’ comes from Latin centr-, meaning centre, and petere, meaning to seek, hence it’s a force that seeks the centre.
  • The net force is always equal to the centripetal force at any point in a circular path.
Centripetal Acceleration:
  • As there is a change in velocity in circular motion, the object experiences an acceleration.
  • This acceleration, known as centripetal acceleration, also always points towards the centre of the circle.
  • The centripetal force needed to maintain an object’s circular motion is directly proportional to the object’s mass and the square of its speed, and inversely proportional to the radius of the circle.
  • The formula to calculate centripetal acceleration is a = v^2 / r, where v is the velocity and r is the radius of the circular path.
Tangential Speed (Linear Speed):
  • Tangential speed or linear speed is the speed of an object moving along a circular path.
  • It is often described in terms of the rotation angle per unit of time.
Period and Frequency:
  • The period (T) of an object in circular motion refers to the time it takes for one complete rotation or revolution.
  • The frequency (f) is the number of rotations or revolutions per unit of time, usually per second.
  • The relationship between period and frequency is f = 1 / T.

Circular Motion Equations

  • Here are the main equations related to circular motion:
    • Centripetal Force: F = mv^2 / r
    • Centripetal Acceleration: a = v^2 / r
    • Tangential Speed: v = 2πr / T
  • Take note of the units used in these equations. Remember to convert them to SI units.

Understanding the Concepts

  • Circular motion concepts become clearer through real-world examples, such as spinning a stone tied to a string, the movement of celestial bodies, or the motion of an electron in a magnetic field.
  • Understanding the forces at work and how the acceleration and velocity of an object in circular motion changes is essential in solving problems.
  • Ask yourself: What would happen if the centripetal force suddenly disappeared? This helps understand its role in maintaining circular motion.

Solving Problems

  • When solving circular motion problems, identify the known and unknown variables.
  • Remember F=ma or Newton’s second law of motion is applicable.
  • Make sure you understand whether the problem is asking for angular or tangential speed.
  • Be careful with unit conversions, especially when dealing with revolutions per minute (rpm) and radians per second.

Remember, practice makes perfect. Understanding circular motion requires continuous learning and solving various problems. Take your time and soon it will all make sense. Happy revising!