Angular Momentum Calculator

Lets consider the planets all revolving around a central point, and lets take a logical explanation for this, so like the planets revolving around the Sun. These are all examples and instances of an object moving around a central point. In this situation, the angular momentum is calculated by product of the mass, m & velocity, v, of the object, and the radius, r, of the circular path that the object is moving along in that particular direction. Hence, we can write the formula of angular momentum as:

L = m*v*r

The Earth's rotation on its axis is an example of a rigid body rotating on its axis without any external force acting on it. In this situation, the angular momentum is calculated as the product of the moment of inertia, I, and the angular velocity, ω.

L = I*ω

By using the formula for angular momentum, the user can easily derive its units by basic dimensional formuals:

L = m*v*r

L = kg ⋅ m/s ⋅ m

L = kg ⋅ m²/s

Hence, the unit of angular momentum is kg ⋅ m²/s. This is the standard unit, however any other respective conversion in all values is logically accepted in the solution.

Conservation of Angular Momentum

The law of conservation of angular momentum states that if no external torque is applied to an object, the object's angular momentum will remain unchanged, this can be explained as follow:

L remains constant when 𝜏 = 0

For any system to obey the law of conservation, an exchange of forces must occur so that the resultant force remains constant and hence the total momentum should be conserved.

This phenomena can be explained in a layman language by considering the example of a ballet dancer, the dancer is swiftly able to stretch their legs in and out by maintaining the angular momentum, hence they dance without falling.

Solved Examples on Angular Momentum

Example 1: An ball with a moment of inertia of 2 kg ⋅ m² rotates at 1 rad/s.And a kid playing with it throws it at a velocity of 7m/s. What is the angular momentum of the ball with which it reaches the ground?

Solution:

Given

Moment of inertia of the ball = 2 kg ⋅ m²

Angular velocity of the ball = 1 rad/s

Linear velocity of the ball = 7 m/s

Angular momentum of the ball is:

The given values suggests we find the solution using the formula:

L = I*ω

L = 2 * 1

L = 2 kg⋅ m²/s

Hence the angular momentum of the ball is 2 kg⋅ m²/s.

Example 2: A 3-kg particle rotates at a constant angular velocity of 2 rad/s. What is the angular momentum if the radius of the circle is 10 cm and the particle is thrown in that circle?

Solution: 

Given

Mass of the object = 3 kg

Radius of the circle = 10 cm = 10/100 = 0.1 m

Angular velocity of the obejct= 2 rad/s

To find:

Moment of inertia and the Angular momentum 

By substituting the values in the given formula of angular momentum

L = I*ω

To determine the moment of inertia for the particle using the formula:

I = m*r²

I = 3 ⋅ (0.1)²

I = 3 ⋅ 0.01

I= 0.03 kg ⋅ m²

Now,

L = I*ω

L = 0.03 ⋅ 2

L = 0.06 kg ⋅ m²/s

Hence the angular momentum of the particle is 0.06 kg ⋅ m²/s.

1. How do you calculate angular momentum?

Linear momentum (p) is defined as the mass (m) of an object multiplied by the velocity (v) of that object: p = m*v.

2. How do you find angular momentum with velocity?

The final angular velocity can be calculated from the definition of angular momentum, L = Iω.

3. What is the angular momentum unit?

Units for angular momentum are kilogram meters squared per second (kg-m2/sec).

4. How do you find angular momentum with torque and time?

An impulse (a torque acting over a time interval) produces a change in angular momentum.

5. What is linear momentum?

Linear momentum is a property of objects which are changing their position with respect to a reference point.