What is Angular Velocity?

Angular velocity is a fundamental concept of physics that describes how objects move in a circular route. Angular Velocity can be understood easily if we include rotation. For example, let’s consider a wheel. A wheel is a circular body that rotates about a fixed axial rod. This motion of the wheel is known as rotational motion. The velocity associated with the wheel as it performs the rotational motion about a fixed axial rod passing through the center is called angular velocity.

A special Greek symbol “ω” which is called omega is used to denote angular velocity in problems.

What Is Angular Velocity?

Angular velocity is a derived physical quantity that belongs to the study of rotational dynamics. Angular velocity is the vector measurement of how speed any object is rotating or revolving around an axis relative to the point from its end has been held.

If an object is performing a rotational motion about an axis, then every point on the surface of that object will be in the rotational motion, and the important part is that the angular velocity of all the parts of that object will be the same. Points at a different distance from the pivot or the axis will have distinct tangential velocity but the angular velocity will be the same.

Angular Velocity Formula

Angular velocity is derived from two other physical quantities, angular displacement and time taken. The angular displacement is also a vector quantity and it is denoted by theta “θ“ and the unit of angular displacement is radians, Hence, you can easily get an idea of what could be the formula for angular velocity.

The SI Unit is radians per unit time.

Angular Velocity = Angular Displacement/ Time Taken

ω = θ/t,

Angular Velocity Centripetal Acceleration Formula

The formula for angular velocity for centripetal acceleration can be derived in a similar fashion just like the derivation of the angular velocity formula. Centripetal acceleration is caused by the change in the centripetal velocity of an object. This acceleration is directed towards the tangent to the circular motion of the object and because of that, the direction of the centripetal acceleration is perpendicular to the radius of the circle.

a_centripetal = v2/r

Average Angular Velocity Formula

The average angular velocity is calculated by obtaining the difference in the angular displacement covered by the object with the time taken for it to complete one rotation.

ω = Δθ/Δt = θ1 – θ2 / t1 – t2

Instantaneous Angular Velocity

The limit function of the averaged angular velocity when the time interval is approaching towards zero is known as the instantaneous angular velocity.

ω_{instantaneous} = dθ/dt

How To Find The Angular Velocity Direction?

Because a point on the surface of a rotating object frequently changes its direction, it’s difficult to detect the angular velocity direction. The rotating object’s axis is the only point on which it has a fixed direction. The Right Hand Rule determines the direction of angular velocity with the help of the axis of rotation.

Right Hand’s Thumb Rule

The right hand thumb rule is utilised to determine the direction of angular motion. Consider a rotating disc for a better idea. As we know,  the axis of rotation is the center of the disc because a pole or any solid rod is passing through the center.

Using the right hand rule, you have to grab the pole or the rod with your right hand in the way that your four fingers follow a rotational direction either clockwise or anticlockwise. Along with that, your thumb has to be perpendicular to your remaining four fingers, pointing straight out along the axis

When you curl your remaining four fingers along the direction of the rotation of the disc, your thumb should be stable because it will point in the direction of motion which the disc is rotating. The plane of the disc at which it is rotating is at the right angle or perpendicular to the direction of angular velocity.

Conclusion

So, if we summarise, angular velocity is a vector quantity which means it has direction along with some magnitude at any given time. Angular velocity formulas are formulated in many different ways such as from the centripetal acceleration, angular displacement, and time taken. There are diverse subsections of angular velocity like instantaneous angular velocity, average angular velocity, etc. Angular velocity has several applications in our day to day happenings. I know you got the basic idea of what is angular velocity, what is the formula for angular velocity, and how we can find the direction vector of angular velocity.