Circular Motion Explained for Class 11 Physics and Beyond

Circular motion in physics refers to an object moving along a circular path or the circumference of a circle. The object's path is at a constant distance from the centre. 

As a curious future physicist or engineer, you must already be wondering more behind the meaning of circular motion. 

• Does the radius of the circle change how an object moves? 
• What type of force pulls it into the circle if the Law of Inertia or Newton's First Law dictates it to go straight?
• Why does speed stay same but velocity must keep changing?
• When does the object come back to where it started?

You will find all these answers in later sections of this guide. 

When it comes to the meaning of circular motion in physics, we must learn that the position vector sweeps out an angle relative to a central point.

This is a key concept when you are studying rotational dynamics in Chapter 6 of Physics Class 11. 

We have three angular quantities that describe the rotational aspects. 

• Angular Displacement ( $\theta$ ) - Angular displacement is the angle swept by the radius (position) vector in a specific time. We measure the angular displacement in radians. It is also an important concept when learning about Simple Harmonic Motion. 
• Angular Velocity ( $\omega$ ) - To understand angular velocity, we have to note that it is simply the rate of change of angular displacement. We denote that by $\omega =\frac{d\theta }{dt}$ . The SI Unit of angular velocity is rad/s.
• Angular Acceleration ( $\alpha$ ): This is the rate of change of angular velocity, given by $\alpha =\frac{d\omega }{dt}$ , in $\mathrm{r}\mathrm{a}\mathrm{d}/{\mathrm{s}}^2$ . For uniform circular motion (a type of circular motion), $\omega$  is constant, and $\alpha =0$ . 

The linear quantities, such as speed, velocity, and acceleration, all relate to the angular quantities when we are describing circular motion. 

• Linear speed: $v=r\omega$ , where $r$ is the radius.
• Tangential acceleration (for non-uniform motion): $a_t=r\alpha$ .

Centripetal force is the real force responsible for the necessary centripetal acceleration to keep an object in circular motion.  It’s directed towards the centre. We denote centripetal acceleration as $a_c=\frac{v^2}{r}$ or $a_c=r{\omega }^2$ .  

Some of the essential examples of centripetal force you can quickly remember are:

• Tension in a string for a stone in circular motion.
• Gravitational force for planetary orbits.
• Frictional force for a car on a curved road.

Centripetal force is a real force directed toward the centre. Centrifugal force is a pseudo (or fictitious) force felt only by an observer in the rotating frame of reference. For FBDs in an inertial frame, just use the centripetal force. Also, check out the differences.

This brings us to another question: ‘What is the difference between uniform and non-uniform circular motion?’

These are two fundamental types of motion within this topic.

• Uniform Circular Motion (UCM): The speed remains constant, but velocity changes due to direction. The only acceleration is centripetal, which is always directed towards the centre.
• Non-Uniform Circular Motion: The speed varies, leading to both centripetal and tangential accelerations. Total acceleration is the vector sum $a=$ $\sqrt[]{a_c^2+a_t^2}$ .
  
  

Brush up on scalar and vector quantities, as well. 

Section 4.10 of the Laws of Motion chapter provides a brief explanation of circular motion as an application of Newton's laws. In the real world, you can learn in this way. 

• Vehicles on Curved Roads: In this scenario, it’s friction that creates the centripetal force. For a car on a level road, we can express that mathematically as $\mu mg\ge \frac{m{v}^2}{r}$

, where $\mu$ is the coefficient of friction.

• Vehicles on Banked Roads: The normal force component provides centripetal force and it is responsible for reducing reliance on friction. The banking angle is $\mathrm{t}\mathrm{a}\mathrm{n}\theta =\frac{v^2}{rg}$