# Circular motion, formula with examples to know.

Circular motion can be defined as the movement of an object while rotating on a circular path. It may be a uniform or nonuniform circular motion.

**What is circular motion?**

Circular motion can be defined as the movement of an object while rotating on a circular path. It may be uniform or non-uniform. In a uniform circular motion, a constant angular rate of rotation and constant speed is maintained by the object, whereas in noncircular motion the rate of rotation keeps changing. Further in such a motion the distance between the object moving and the fixed point on the surface remains constant all the time**.**

### Some examples;

- An artificial satellite orbiting the earth in its specified orbit.
- A moving wheel of a running vehicle.
- The blades in a windmill when in motion.
- A ceiling fan when moving.
- Moving electrons around the nucleus.

An object sets in a circular motion means it has to cover the circumference of a circular path. Thus the basic aspect of this motion is the change of its direction continuously, which is not seen in** linear motion.** As it changes direction means the change of acceleration by the influence of **a centripetal force** in the direction of the center of rotation, the force that keeps an object bound to follow a circular path.

### Uniform circular motion;

In such motion, an object traverses a circular path with constant speed but its velocity varies. Velocity is a vector quantity that depends on both speed and direction of travel. Variable velocity indicates the presence of acceleration. Here the acceleration has a constant magnitude which always points towards the center of the rotation and is always perpendicular to the velocity of the object as shown in Image A.

The object complies with repeated trips around the route in the same amount of time every time. Further, as the object is in circular motion its distance from the axis of rotation remains the same at all times.** **In this motion, the total acceleration of an object moving in a circular path is equal to the radial acceleration. The acceleration of the object in the circular path is called **radial acceleration**, as it has a certain radius from a central point. It is also known as **centripetal acceleration.**

#### Formula;

For motion in a circular path, its radius is** R,** and the circumference of the circle is **C**. Now C is represented as** 2πr**

**or C= 2πr. **

If the period of one rotation is **T**, then the **angular velocity,ω** is

**ω=2π/T=2πf=dθ/dt **

and the units for angular velocity are radians/second (rad/sec).

If the magnitude of the velocity of the object is **V**, then the radial acceleration of the object can be

**α _{rad}=v^{2}/r**

It is to mention here that radial acceleration is always perpendicular to the direction of the velocity. SI unit of radial acceleration is **m ^{2}s^{-2}**.

The speed/velocity of the object in a circular motion can be equal to the circumference **C** of the circle divided by the period(time taken by the object to cover the distance)represented as;

**V=C/T=2πr/T**=**ωr **

The angular acceleration **α** of the particle can be written as,

**α=dω/dt**

Acceleration is defined as the change in velocity either in magnitude or direction or both. In uniform circular motion **α** remains zero, and the equation can be

**α _{c}=v^{2}/r=ω^{2}r **

**Radial acceleration becomes greater at high speeds and in sharp curves.**

### Nonuniform circular motion;

Nonuniform circular motion is a type of circular motion in which the speed of the object varies without any uniformity. Both the velocity and acceleration of the object in such a motion fluctuate. Since the speed changes, here** tangential acceleration **along with normal acceleration is experienced and is non-zero. Image B

However additional forces acting on the object are seen due to non-zero tangential acceleration.** **Unlike uniform circular motion in such cases, acceleration did not change in regular intervals.

#### Some examples;

- A car is struck in a traffic jam on a circular road.
- Roller coaster
- The motion of a vehicle on a vertical circle.
- Windmill.
- Tires of a bicycle.

#### Formula;

In a nonuniform circular motion, additional forces act due to non-zero tangential acceleration along with a centripetal force. However, in spite of the additional forces acting upon the object moving in the circular path, the sum of all the forces can be equal to the centripetal force and the equation is as such;

**F _{net}=mα=mα_{r}=mv^{2}/r=F_{c}**

So far the acceleration concerned,** **in such a type of motion has two components like tangential acceleration **α _{T}**

_{ }and radial acceleration

**α**

_{R.}It is due to the radial component the change of the direction of the velocity happens but the magnitude of the radial acceleration is the same as uniform circular motion. Now the equation is,

**α**_{R}**=v ^{2}/r**

Where the speed fluctuates, then the tangential component is the cause of the change of magnitude of the velocity of an object. The equation is;

**α _{T}**=

**dv/dt**

Hence the total acceleration is** √(α ^{2}**

_{r}+

**α**

^{2}_{t)=}α**Bottom line;**

The circular motion includes both uniform and non-uniform types. The object’s speed in uniform circular motion is constant, whereas in non-uniform type it varies. Further, the **tangential acceleration **along with normal acceleration is zero in the former type of motion but non-zero in the latter type. In the uniform type of circular motion, the magnitude of centripetal force is always zero but it is non-zero in the non-uniform type, and we experience the above motion in our day-to-day life very often.

## 8 Comments

All are in a systematic way and very easy to understand.

Thankyou 👍

Nice one 👍

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