🌪️ Angular Momentum Calculator
Calculate rotational momentum
How to Use This Calculator
Enter Mass
Input the mass (m) of the object in kilograms (kg). This is the mass of the rotating or orbiting object. For example, a 2 kg mass rotating around a point.
Enter Velocity
Input the linear velocity (v) of the object in meters per second (m/s). This is the tangential velocity, which is the speed of the object as it moves in its circular path.
Enter Radius
Input the radius (r) in meters (m). This is the distance from the center of rotation to the object. For circular motion, this is the radius of the circular path.
Calculate and Review
Click the "Calculate" button to compute the angular momentum. The result will be displayed in kg·m²/s. Angular momentum is conserved in isolated systems, making it a crucial quantity in physics.
Formula
L = mvr
Where:
• L = Angular momentum (kg·m²/s)
• m = Mass (kg)
• v = Linear velocity (m/s)
• r = Radius (m)
Alternative form using angular velocity: L = Iω, where I is moment of inertia and ω is angular velocity.
Example 1: Orbiting Satellite
A 500 kg satellite orbits Earth at 7500 m/s at a radius of 6,700,000 m from Earth's center. Calculate its angular momentum.
Given:
• Mass (m) = 500 kg
• Velocity (v) = 7500 m/s
• Radius (r) = 6,700,000 m
Solution:
L = mvr
L = 500 × 7500 × 6,700,000
L = 25,125,000,000,000
L = 2.51 × 10¹³ kg·m²/s
Example 2: Spinning Ball
A 0.5 kg ball on a string moves in a circle with radius 2 m at 10 m/s. What is its angular momentum?
Given:
• Mass (m) = 0.5 kg
• Velocity (v) = 10 m/s
• Radius (r) = 2 m
Solution:
L = mvr
L = 0.5 × 10 × 2
L = 10 kg·m²/s
Frequently Asked Questions
What is angular momentum?
Angular momentum is the rotational equivalent of linear momentum. It measures the "quantity of rotational motion" an object has and is conserved in isolated systems. It's a vector quantity measured in kg·m²/s, describing how much rotational motion an object has around a point or axis.
What is the conservation of angular momentum?
The conservation of angular momentum states that in an isolated system (no external torques), the total angular momentum remains constant. This is why ice skaters spin faster when they pull their arms in (reducing moment of inertia) and why planets maintain their orbital characteristics.
How is angular momentum different from linear momentum?
Linear momentum (p = mv) describes motion in a straight line, while angular momentum (L = mvr or L = Iω) describes rotational motion. Angular momentum depends on both the distance from the rotation axis and the velocity, making it fundamentally different from linear momentum.
Can angular momentum be negative?
Yes, angular momentum can be negative, depending on the coordinate system and direction of rotation. The sign indicates the direction of rotation (clockwise or counterclockwise). However, the magnitude (absolute value) is what's most often physically meaningful.
What is the relationship between angular momentum and moment of inertia?
Angular momentum can also be expressed as L = Iω, where I is the moment of inertia (rotational mass) and ω is angular velocity. This form is more general and applies to extended objects rotating around an axis, not just point masses.
Where is angular momentum used in real-world applications?
Angular momentum is crucial in: understanding planetary motion and orbital mechanics, designing gyroscopes and navigation systems, analyzing spinning objects in sports (figure skating, diving), satellite and spacecraft design, understanding atomic physics and quantum mechanics, and designing rotating machinery and engines.
About Angular Momentum Calculator
The angular momentum calculator computes the rotational momentum of an object using L = mvr. Angular momentum is a fundamental conserved quantity in physics, crucial for understanding rotational motion, orbital mechanics, and many physical phenomena.
This calculator is essential for students studying rotational dynamics, engineers designing rotating systems, and anyone analyzing circular or orbital motion. Angular momentum conservation is one of the most important principles in physics, explaining everything from why ice skaters spin faster when they pull their arms in to how planets maintain stable orbits.