A Level Physics: Motion in a Circle and Orbits Explained

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The study of circular motion is important in physics because all the planets, moons, stars, comets and other heavenly bodies move in a circular path. Scientists cannot put a satellite in orbit without precisely calculating its circular motion. Not only that, most of the mechanical machines we use have parts that move in a circular path, such as wheels of cars. To have a deeper understanding in this study, you can engage in physics tuition to help develop your knowledge.

Definition of Circular Motion

The movement of an object on a circular path is called circular motion. What this means is that the moving object makes an arc of a circle. Circular motion is classified as uniform circular motion and non-uniform circular motion.

  • Uniform circular motion: When an object moves on a circular path with a constant speed, it is called uniform circular motion.
  • Non-uniform circular motion: When an object moves in circular path with varying speed, it is called non-uniform circular motion.

The implication of Newton’s Laws on Circular Motion

Newton’s first law of motion states that an object moving in a straight line will continue to move in the same line unless an external force compels it to change its action. But what about an object moving in a circle? Obviously, there must be some force working on it to change its direction. In the case of the planets, it is the gravitational force of the sun.

Newton’s second law of motion states that force is equal to the change in momentum per change in time. What this means is that an object acted upon by a force will accelerated in the direction of the force. The implication of this law for circular motion is that force cannot have components that are in the direction of velocity. Rather, the force is perpendicular to the velocity of the object.

Therefore, acceleration in uniform circular motion is always perpendicular to the trajectory. However, in the case of non-uniform circular motion, the component of the force remains in the direction of velocity.

Angular displacement

As mentioned earlier, an object that is in a circular motion traces the arc of a circle. The angle subtended by the end of the arc with the radii at the beginning of the arc is known as the angular displacement of the object.

This is mathematically represented by the equation q = s / r (there must be a right arrow above q and s to show that they are vector quantities), where s is the length of the arc and r is the radius of the arc. The SI unit for the measurement of angular displacement is radian. 1 radian = 180/p degrees.

If angular displacement exceeds 2p radian, it means the object has completed more than one revolution. For this reason, angular displacement can be considered as an angular distance.

Angular velocity

Angular velocity of an object in circular motion is the rate of change of angular displacement. It gives the rate of an object in circular motion tracing an arc.

This is mathematically represented by the equation w = q / t (w and q must have a right arrow above them to show that they are vector quantities), where q is the angular displacement and t is the time taken. The SI unit for the measurement of angular velocity is radian per second (rad/s).

Period and frequency

The time taken by an object in circular motion to complete one revolution is called period of circular motion. The number of revolutions completed per second is called the frequency. The mathematical formula for frequency is f = 1 / T. The SI unit to measure frequency is Hertz, which is equivalent to 1 s-1 (1 inverse second).

Motion in circle and orbits is not easy to master. You may need to take an A level physics or a well-known tuition centre in Singapore to excel in physics.