# 19+ Conservation Of Angular Momentum Examples: And Problems

Conservation of angular momentum describes the spinning property of a physical system in which the spin remains constant unless an external torque disturbs the system’s spin.

A list of conservation of angular momentum examples is given below.

## A detailed explanation of conservation of angular momentum examples

Angular momentum is a product of momentum inertia of rotational object times the angular velocity. It is also characterized by two other types: spin angular momentum and orbital angular momentum based on the orientation of rotation. This section gives a brief explanation regarding conservation angular momentum examples.

## The spin of a figure skater

When a figure skater begins to spin on an ice rink with one arm extended, as soon as they spin faster with greater angular velocity and the arms are drawn inward, the moment of inertia is reduced; thus, angular momentum is conserved.

## Point mass rotating through the hollow tube

Tie a point mass to one end of a string and rotate it in a vertical hollow tube; the point mass rotates in a horizontal circle with the constant angular momentum.

If the string is pulled down, the radius of the rotational axis reduces, and the torque will be zero; thus, angular momentum is conserved as the force acting on the point mass, and the string is radial.

## Man on a rotating table holding a dumbbell

To explain the conservation of angular momentum examples assume that a man outstretches his arm holding a dumbbell and stand at the center of the rotating table.

When he pulls his arm inward, the speed of the rotational table increases as the distance between the center of rotation and the dumbbell decreases, which leads to an increase in the angular velocity and a decrease in the moment of inertia, thus the angular moment will remain constant being conserved.

## Diver jumping to the water from height

A diver jumps to the water from a springboard by pulling his arms and legs towards the center of his body. By this action, the body’s moment of inertia decreases by subsequent angular velocity. The above action helps him to rotate his body in the air. So he does not keep his hand straight.

## Gyrocompass in an airplane

Airplanes are fitted with the gyrocompass to relocate the geographical direction for navigation based on earth rotation. The gyrocompass consists of a spinning disc.

A spinning gyrocompass rotates freely independent of the aircraft’s motion, and its orientation remains constant. Thus the angular momentum of the gyrocompass is conserved in the airplane.

## Propellers of the helicopter

A helicopter is provided with two propellers to balance the conservation of angular momentum.

If a helicopter is fitted with only one propeller, the helicopter body would have turned opposite to the direction of the propeller’s rotation due to the conservation of angular momentum. Thus for stability, two propeller shaft is required.

## Rotational collision of two objects

Conservation of angular momentum in the rotational collision of two objects is an excellent way to explain the conservation of angular momentum examples.

Let us illustrate by considering an example. Suppose a ball collides with a stick, then the ball rotates at its end. When two objects collide, an angular impulse is exerted on both objects, which is equal and opposite to maintaining the total angular momentum constant.

## Rotation of the earth

The angular momentum of the earth is fairly conserved while rotating because the earth exerts a gravitational force, which is a central and conservative force.

## Moon revolving around the earth

The moon revolving around the earth possesses constant angular momentum due to the earth reducing its angular momentum due to drag or friction applied by the tides, which is gained by the moon. So the angular momentum is conserved on the moon.

## Spinning the ball on a fingertip

When a ball is made to rotate on the fingertip, the total angular momentum of the ball is conserved until and unless an external force is triggered on the ball.

## The spinning of top toys

When a top toy is made to spin, it gains angular momentum. This remains constant until an external torque is applied to it. The angular momentum gradually decreases due to friction between the surface and top toy.

## Wheels

The angular momentum is associated with the wheels, such as the bicycle wheel and the rotating chair’s wheel.

When the wheel is subjected to spin, the torque acting on the wheel is nullified. Thus, the angular moment does not change and is conserved if the wheel rotates continuously.

## Ballet dancers spin

The position of the ballet dancer during their performance involves stretching their arms and legs inward and outward while spinning. This action consequently increases or decreases the angular momentum and moment of inertia, thus conserving the angular momentum.

## Bowling game

In the bowling game, the ball moves over the ramp by rotating and hits the pin, making it fall. The ball’s angular momentum after hitting the pin is also balanced by decreasing its moment of inertia.

## Gymnast

Gymnasts are aware of the conservation of angular moment during their exercise. They have to curl their body towards their center of mass during the floor exercise, which is carried by conserving the angular momentum.

## Asteroids spinning freely in space

Asteroids rotating freely in space have constant angular momentum as external torque would influence them.

## Speed of wind in Tornadoes

In the inner layer of tornadoes, the speed at which the wind rotates is restricted by the law of conservation of angular momentum. They spin rapidly and gain angular velocity, leading to losing the moment of inertia. Hence the angular momentum is conserved.

## The spin of an electron

The angular momentum demonstrates the electron revolving around the nucleus. Electrons also orbit around the nucleus. Their spin angular momentum is conserved in every aspect of spinning.

## Planetary motion

All the planets around the sun in an elliptical orbit have constant angular momentum.

From Kepler’s second law of planetary motion, its mass remains the same, but the distance between the planet and the sun varies as the planet goes nearer to the sun and its speed increases. Thus angular momentum is conserved in planetary motion.

## Gyroscope

In a gyroscope, the tendency of a rotating object to orient in a rotational axis must possess constant angular momentum. The gyroscope acquires the angular momentum in the torque direction and rotates on the horizontal axis.

## Conservation of angular momentum problems

The angular momentum of any object is associated with angular velocity and the moment of inertia. Let us solve some conservation of angular momentum examples problems using all of them.

## A ballet dancer has a moment of inertial of 3kgm2 when the arm is pulled inward and 10kgm2 when the arm is stretched outward. If the rotational speed of the dancer when the arm is inward is 14round/sec, calculate the dancer’s speed when the arm is stretched outward.

Solution:

Since the angular momentum is the product of the moment of inertia and angular velocity, we can write the equation as

Iω=Isωs

3×14=10×ωs

42=10ωs

ωs=4.2rounds/sec.

## A man is standing on a turntable rotating with angular velocity ω and moment of inertia of I with his arm towards the center of the body. When he extended his arm outward, the moment of inertial is increased by 4 times its original value. Calculate the new angular velocity.

Solution:

The conservation of angular momentum is

Iω=I’ω’

Let I and I’ be the moment of inertia when the arm is inward and extended, respectively, and ω and ω’ be the angular velocity when the arm is inward and extended, respectively.

I’=4I

Iω=4Iω’