Angular Acceleration

The angular acceleration is the rate at which the angular velocity changes over time and is generally stated in radians per second squared. Generally when θ=ωt and α=0 The angular velocity is uniform.

Acceleration

An acceleration is the rate of change in velocity w.r.t time. Similarly, the second derivative of position with respect to time can be used to describe acceleration. It’s a vector quantity, which means that it has both a magnitude and a direction. The letter ‘a’ stands for acceleration.

Meters per second square or metres per second per second or m/s2 is considered as the unit of acceleration.

Types of acceleration

Uniform acceleration

A body is considered to be uniformly accelerated if it is travelling in a straight line and its velocity rises in absolutely regular intervals of time. Because the object’s velocity increases at a consistent pace, it’s also known as constant acceleration.

When a car travels at a constant speed on a straight path and then suddenly slows or turns right or left, it loses its uniform acceleration. The car is no longer accelerating at a consistent rate.

A free-falling body is an example of uniform acceleration. If you fall over a bridge or the top of a building, the acceleration you experience is solely due to gravity.

Equation for the uniform acceleration is given as,

s=ut+1/2at2 

Here,

U = initial velocity of body

a = Acceleration

t = time

Non-uniform acceleration

Uniform acceleration is the reverse of this motion. If a body’s velocity rises in random quantities at fixed intervals, it is said to be moving in a non-uniform acceleration. The change in speed is not stable in this case; it is constantly changing. Moreover, the amplitude and direction of acceleration may change.

For example -Non-uniform acceleration can be seen in a car moving in traffic jams or a child riding a bike on an elevated road. 

Average acceleration

As we know, acceleration is the speed at which the velocity varies. A certain time period is represented by average acceleration. This will be based on the change in velocity over a fixed period of time.

For example, when the velocity of a speeding bicycle’s rises between 0 to 120 cm/s in 6 seconds, then the bicycle’s average acceleration is 20 cm/s2. It shows that the bicycle’s speed is increasing at a rate of 20 cm/s..

Instantaneous acceleration

Instantaneous acceleration is the acceleration of an object at any given time. Acceleration gets zero or slowdown when velocity decreases. Likewise, if speed is constant, the acceleration will be high.

Centripetal or circular acceleration

The acceleration of a body travelling in a circular direction is known as centripetal acceleration. The direction of its circular motion varies frequently, forcing the velocity to differ. Like a response, an acceleration force is generated, which is directed to the centre.

If you spin a ball around with a rope, it generates centripetal acceleration. Likewise, when you’re on a merry-go-round and it is spinning, you’re experiencing centripetal acceleration.

Equation of circular acceleration

ac =v2/r 

Here,

ac= centripetal acceleration

v = velocity

r = radius

Angular Acceleration

The actual rate of change of angular velocity, generally indicated by and expressed in radians per second squared, is called angular acceleration. Moreover, because the angular acceleration increases linearly with time, it is constant and does not depend on the time variable.

The symbol alpha is used to denote angular acceleration, which is measured in units of angle per unit time squared (radians per second squared in SI units).

Now, angular acceleration is defined as the rate of change of angular velocity over time and is generated from angular velocity. Rotational acceleration is also another name for angular acceleration.

The Angular Acceleration can be calculated by using this formula:

α=dω/dt

Here,

α= Angular Acceleration

ω=Angular velocity

t = Time

dω= Change in angular velocity

dt = Change in time

Formula of Angular Acceleration

If the change in angular velocity is not constant and changes from time to time, we can use a different formula.

The formula is given as 

avg= ω2–1d2–d1

Here,

avg=Average angular acceleration 

1=Initial angular velocity 

2=Terminal angular velocity 

d1=Initial time 

d2=Terminal time 

Because angular acceleration is a vector, it has a directional component. To determine the direction of the angular velocity, we must first identify the rotational direction of the body. The direction of the angular velocity is moving away from you if the body is rotating in a clockwise direction. The direction of the angular velocity is moving towards you if the body is rotating or travelling in a counter-clockwise direction.

 Angular Velocity

To understand what angular acceleration is, it is important to understand angular velocity. The rate of change in displacement of a body that is rotating around a fixed point in a circular pattern in a particular time period is known as angular velocity. The Greek letter omega, i.e., is used to represent angular velocity.

The Angular velocity can be calculated by using this formula:

ω=v/r

Here,

ω=Angular velocity

v=linear velocity 

r = radius

                                                                                                                                                                                                                      Types of Angular Acceleration

1. Spin Angular Acceleration
2. Orbital Angular Acceleration

Spin Angular Acceleration

The angular acceleration of a rigid body about its centre of rotation is known as spin angular acceleration. The angular acceleration of a solid object around its axis of rotation is known as spin angular acceleration, while the rotational motion of a single object around a fixed point is known as orbital angular acceleration.

Orbital Angular Acceleration

The angular acceleration of a point particle around over a fixed origin is known as orbital angular acceleration. The speed at which a solid body rotates around a given source, or the actual rate at which its angular motion varies respect to the source, is known as orbital angular velocity

Conclusion

The actual rate of change of angular velocity, generally indicated by and expressed in radians per second, is called angular acceleration.  Angular acceleration is also defined as the rate of change of angular velocity over time and is generated from angular velocity. Rotational acceleration is also another name for angular acceleration.

The formula is given as

avg= ω2–1d2–d1

The rate of change in displacement of a body that is rotating around a fixed point in a circular pattern in a particular time period is known as angular velocity.

The Angular Acceleration can be calculated by using this formula:

ω=v/r