Suppose a particle is moving in a circular motion and we have to understand about its scalar components. In a generalized sense, those dual components are acceleration and velocity.

Let the 2 points of the straight line D and P be the half of the circular motion.

Let r, which is the radius of that circular path, be constant.

As per this information, calculations for both acceleration and velocity are:

v =r θ

an =v2/r = r θ 2 = v θ

at = dv/dt = v = rθ

Here, the measurement of ‘e’ is done from any side of convenient radial reference which then goes to DP.

Angular Velocity

The rate of change of a rotating particle body in an angular position is known as the angular velocity of that particle.

Angular velocity is represented as w

Equation for angular velocity is,

W = dθ/dt

According to another figure of a particle moving in a circular motion, its linear velocity is represented as,

Linear velocity= r x angular velocity

The next equation stands at, v rθ = rw

Unit of angular velocity (w) = rad /s

Angular Acceleration

The rate of change of angular velocity is known as angular acceleration.

Its equational definition is,

a = dw/dt = d2θ/dt2 = θ = w

Equation for tangential equation is,

at = dv/dt = v = rθ

This calculation further goes to,

= r w = r dw/dt

= ra

In case of normal acceleration, its equation is,

v2/r = w2r2/r = w2r

Derivational equations for linear velocity are applicable for angular velocity.

If a certain instance is taken, equation for angular velocity is,

w = w0 +a tà

Equation for linear velocity is,

v = v0 +atà

**Links of Previous Main Topic:-**

- Introduction about distributed forces
- Area moments of inertia in rectangular and polar coordinates
- Mass moment of inertia introduction
- Work done by force
- Kinematics of particles
- Position vector velocity and acceleration
- Rectangular components of velocity and acceleration
- Projectile motion
- Tangential and normal components of acceleration
- Radial and transverse components
- Special case circular motion

**Links of Next Mechanical Engineering Topics:-**