# 11 Angular Acceleration Examples: Detailed Insight And Facts

In this article, we will see various angular acceleration examples with detailed insight.

An object exhibiting circular motion associates the angular acceleration. The following is the list of examples of angular acceleration:-

## Electric Motor

The electric motor runs on the principle of electromagnetism. When supplied with the electric current, the coil in the motor produces the magnetic field that experiences the torque and the motor rotates. It helps to convert electric energy into mechanical energy. The speed of the motor is calculated as the rotation per minute (rpm).

## Merry-go-round

A person sitting on the merry-go-round experiences the centripetal force acting towards the point at a center, and the centrifugal force outward. Both the forces cancel out, which keeps the body intact on the seat and in the direction of motion.

There is a change in the angular velocity of the merry-go-round while speeding up and slowing down the wheel. The direction of the radial velocity of a person keeps on changing which is proportional to the angular velocity and the distance of a chair on which the person is seated from the center of a merry-go-round.

## Ferries wheel

The ferries wheel accelerates at a constant speed, and its speed varies only at the start of the journey and at the end to slow down. Since, there is a change in the angular velocity of a ferries wheel, while speeding up or down it is associated with the angular acceleration; otherwise, it has a constant angular acceleration.

We can write a kinematics equation for the angular velocity of the ferries wheel as

Integrating the above equation,

Squaring eqn(1) on both the sides

From eqn(2),

Using this in the above eqn, we have third kinematic equation.

## Mixer

Due to the rotation of the shaft attached to the blades used in a mixer, the blades rotate to grind the mixer. The speed of the motor is regulated by the power supplied to the machine that increases or decreases the rotations per second of the motor couplers. As the angular velocity of the motor coupler varies, the rate of angular acceleration varies accordingly.

## Grinder

A shaft on the machine rotates on supplying the electric current that results in the rotors attached to the shafts to accelerate. One rotation of a rotor will displace the outer vessel which is filled with the mixture to a length of the circumference of the rotor.

The angular velocity of the grinder varies on changing the power supply while starting the machine and on putting off from the power supply.

## Gravitron

The angular velocity of the gravitron rises gradually and constantly until the centrifugal force acting on the body reaches the epic point at which, even after removing the plate beneath the foot of a person standing in the gravitron does not fall down due to gravity.

This is an exciting thing to experience at the amusement park. The speed of a gravitron varies constantly and hence there is an angular acceleration of the gravitron. The centrifugal force is responsible for a body to remain attached to the wall of the gravitron and prevent a person from falling down underneath.

## Wheel of a Car

The angular velocity of a wheel depends upon the speed of a car. The angular acceleration of a wheel is equal to the change in the angular velocity of a wheel.

The distance covered by one revolution of a wheel of a car is equal to the circumference of a wheel. The greater the diameter of a wheel less will be its angular velocity and hence less will be the angular acceleration by the wheel.

## Fans

On putting on the power to the fan, the propellers initially rotate because of the energy stored in the capacitor of the fan, and then gradually take the speed as the motor of the fan experiences the torque due to the electromagnetic field.

The speed of the rotation of a propeller is regulated by the regulator and changes by switching the plug for different power ranges. We see the variations in the angular velocity of the fan, hence is an example of angular acceleration.

## Windmills

Windmill converts wind energy to electric energy. For propellers of the windmill to rotate a shaft is connected to the propellers and which is then connected to the motor to increase the number of rotations of a propeller to produce a large amount of energy. The electric energy produced is stored in the generator.

The energy produced depends upon the number of turns of a propeller which is governed by the angular speed that keeps on varying with the speed of the wind. Hence, the acceleration rate of the propellers varies.

## Pulley

A pulley is a wheel that is designed for easy displace or lift the objects to minimize the utilization of the muscular force by changing the direction of the force applied.

The angular acceleration of a pulley depends upon the angular velocity of a pulley varied with time. The pulley accelerates by stretching the length of the string attached to the pulley.

## Pendulum in a Simple Harmonic Motion

A pendulum in a harmonic motion oscillates with angular velocity making an angle between the initial and final highest point which reduces with time. The speed of the pendulum also decreases due to the restoring force and the air drag.

There is a continuous change in the angular velocity of a pendulum which decreases with time; hence the angular acceleration of a pendulum in a simple harmonic motion is negative.

Read more on How To Find Constant Angular Acceleration: Problems And Examples.

## Q1. The ferries wheel at a rest starts accelerating with an angular velocity of 4m/s in 8 seconds. What is the angular acceleration of the ferries wheel?

Given:

ωf = 4m/s

ωi = 0

t= 8s

ωf = ωi + α t

4= 0+ α * 8

α = 4/8 = 0.5 m/s2]

## Q2. Consider an object in a rotational motion. The angular displacement of the object is given by the equation θ = 3πt2 + πt + 6π + 2 Find the angular velocity and angular acceleration of the object.

Given:

The angular velocity is given by

The angular acceleration of the object is

## What is orbital angular acceleration?

An object moving in an orbital motion with focus at the center making an angle θ on displacement.

The change in the angular velocity of the object in an orbital motion due to varying angles with respect to time is called the orbital angular acceleration.

Click to read more on 16+ Change In Acceleration Examples.

AKSHITA MAPARI

Hi, I’m Akshita Mapari. I have done M.Sc. in Physics. I have worked on projects like Numerical modeling of winds and waves during cyclone, Physics of toys and mechanized thrill machines in amusement park based on Classical Mechanics. I have pursued a course on Arduino and have accomplished some mini projects on Arduino UNO. I always like to explore new zones in the field of science. I personally believe that learning is more enthusiastic when learnt with creativity. Apart from this, I like to read, travel, strumming on guitar, identifying rocks and strata, photography and playing chess. Connect me on LinkedIn - linkedin.com/in/akshita-mapari-b38a68122