## Learning Objectives

## After completing the topic, the student will be able to:

- Define and discuss circular motion and its types extensively.
- Discuss and relate tangential and rotational speed with relevance to their importance in circular motion of the objects.
- Define, discuss and extend the concept of centripetal force to real world applications.
- Define, distinguish and differentiate between projectile motion and uniform circular motion.
- Understand and evaluate the direction of force at every point, in a circular motion.
- Understand and employ the concept of centrifugal force to the real world applications.
- Identify the use of centrifuge to separate components that are present in a homogeneous mixture.
- Understand, probe and apply the concept of banking of roads to the real world situations.
- Discuss the motion of an object in a vertical circle and explore its applications in everyday science scenarios.

Circular motion is a movement of an object along the circumference of a circle or rotation along a circular path or a circular orbit. The rotation around a fixed axis of a three–dimensional body involves circular motion of its parts but it is assumed as motion of a point mass in a plane. Hence the center of mass of a body is considered to undergo circular motion. It can be uniform, that is, with constant angular rate of rotation or non–uniform with a changing rate of rotation. Examples of circular motion: Satellite orbiting the Earth at constant altitude, a car turning through a curve in a race track, an electron moving perpendicular to a uniform magnetic field, and a gear turning inside a mechanism.

When a particle moves in a circle with constant speed, the motion is called uniform circular motion. A car moving at constant speed along a circular path, satellite moving in a circular orbit are examples of uniform circular motion. The direction of acceleration changes continuously so that it always point towards the center of the circle but the magnitude of acceleration remains same at all times.

At the top of the circle, the acceleration points down and at the bottom of the circle the acceleration points up. Such change in direction of velocity involves acceleration of the moving object by a centripetal force, which pulls the moving object towards the center of the circular orbit. A roller coaster car that slows down and speeds up as it moves around a vertical loop is an example of non-uniform circular motion in which the magnitude of acceleration also changes along with direction.

In Newton’s laws of motion, we have seen that an unbalanced force is necessary for change of motion. No net force is acting on a body, which is undergoing uniform motion (uniform velocity). Then we introduced the concept of friction. We showed that friction is necessary for motion. To overcome kinetic friction (sliding or rolling friction), we need the extra net force even when a body is in motion. For a frictionless motion, no unbalanced force is necessary. But in practical everyday situations, frictionless surfaces do not exist! Thus a net force is a must for all motions.

Initially we have discussed linear motion. If force is necessary for motion, then in linear motion, force and acceleration are in the same direction. Velocity could be parallel or anti–parallel to acceleration, but in one line. We soon upgraded our knowledge and discussed two–dimensional non–linear motion.

In circular motion we encountered a strange fact, strange because it is contrary to our knowledge of direction of force, acceleration and velocity. In circular motion, the force and acceleration are pointed towards the centre of the circle, but the velocity is tangential to the circle. That means acceleration and velocity are at right angles to each other ! This is where the confusion arises in every learner’s mind. Let us try and answer why this happens in case of circular motion (uniform or non–uniform circular motion).