## Circular Velocity

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# Circular Velocity Calculator

Have you ever observed a rotating fan or a wheel of a moving bicycle? Every point on them undergoes circular movement about the center of rotation. Such a motion of particles where the movement of an object is in a circular path is called as circular motion.

### What is uniform circular motion?

Any particle that moves in a circle with a constant speed is said to be under uniform circular motion. The main aspect of uniform circular motion is that the direction of the particle keeps changing all the time at every instant. The direction of the particle is in the instantaneous tangential direction.

To say, in a uniform circular motion, the direction always keeps changing, but the magnitude of the circular velocity remains constant at every instant.

### Can there be non-uniform circular motion?

Yes, there can be. In such type of non-uniform circular motion, the velocity of the particle is not constant. For example, when you spin an object tied to a rope in a vertical circle fashion, you must have noticed that the motion is faster when the object is at the bottom, where gravity adds to its speed and slower at the topmost position, where gravity acts against to it.

Another special kind of circular motion is when an object rotates around itself also known by spinning motion. A spinning top is an example of this type of circular motion.

I shall now recall to mind that the motion of the heavenly bodies is circular since the motion appropriate to a sphere is rotation in a circle. – Nicolaus Copernicus

### Variables in Circular Motion

The motion of a particle undergoing circular motion is defined by a certain set of variables as defined below:

#### Angular Displacement:

Denoted by Δθ, this is the angle that the position vector of a particle makes at the center of the path of the circular motion.

It is also the ratio of linear displacement and the radius at any given instant of time. The unit of angular displacement is radian.

Angular Displacement (Δθ) = (ΔS/r)

#### Angular Velocity

It is the rate of change of angular displacement (Δθ). It is measured in rad/s and it is a vector quantity.

Angular Velocity (ω) = Δθ/Δt

#### Angular Acceleration

It is the rate of change of angular velocity (dω). It is measured in rad/s2 and it is a scalar quantity.

Angular acceleration (α) = dω/dt = d2θ / dt2

#### How is circular velocity calculated?

The formula for calculating circular velocity formula is:

v_{c} = 2πr / T

Where r is the radius of the circular orbit

T is the time period.

In case you know angular velocity ω, then you can calculate circular velocity as:

v_{c} = ω r

Where ω is the angular velocity,

r is the radius of the circular path

#### Sample Problem to understand circular velocity calculation

Calculate the circular velocity of a stone tied to a thread of 1 m when it is swirled with the angular velocity of 45 radians/s

Solution

Here:

Angular velocity ω = 45 rad/s

radius = 1 m

We know that the circular velocity formula is given by v_{c} = ω r

v_{c} = 45 × 1

= 45 m/s.

Examples of Uniform Circular Motion

- Stone tied to a rope and swirled horizontally
- The hands of a clock
- A circular object moving on a floor with constant velocity
- The tires of a road roller or a car moving with a uniform speed
- Rotating blades of a ceiling fan.
- An artificial satellite rotating around the earth at a fixed height.
- Electrons in an atom moving around the nucleus.
- A merry go round

### Do you know?

Newton’s law applies to circular motion too. Let’s see how:

According to Newton’s first law of motion, any object will continue to be in a state of motion unless acted upon by an external force. In case of circular motion, this force is nothing but the centripetal force or the force that keeps pulling the body towards the center.

For instance, when you spin a stone tied to a rope by holding with your hand, your hand is exerting centripetal force on the stone through the rope. It is this force that keeps the stone moving circularly. Interesting, isn’t it? To learn more about centripetal force, check out our centripetal acceleration calculator page.

### How CalculatorHut’s online free circular velocity calculator helps you?

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Circular velocity is an indispensable concept for any physics student. With the help of our calculator, you can easily calculate any parameter of the circular velocity formula and get instant results. CalculatorHut’s free circular velocity calculator is also a useful tool for cross verifying the results that you obtain during calculations and learning the concepts of circular motion.

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Gravity explains the motions of the planets; but it cannot explain who sets the planets in motion. – Isaac Newton.