How is Torque Related to Angular Momentum? A Simple Guide

^{Torque and angular momentum are two important concepts in physics that describe the motion of rotating objects. In this article, we will explain what torque and angular momentum are, how they are related, and why they are important for understanding the behavior of spinning things.}

^{What is Torque?}

^{Torque is a measure of how much a force applied to an object causes it to rotate. It is also called the moment of force or the rotational force. Torque is a vector quantity, which means it has both magnitude and direction. The magnitude of torque depends on three factors:}

• ^{The magnitude of the force applied to the object}
• ^{The distance from the axis of rotation to the point where the force is applied}
• ^{The angle between the force and the lever arm (the line connecting the axis of rotation and the point of force application)}

^{The direction of torque is perpendicular to both the force and the lever arm, and follows the right-hand rule: if you curl your fingers in the direction of the force, your thumb will point in the direction of the torque.}

^{The formula for torque is:}

^{�=�×�τ=r×F}

^{where �τ is torque, �r is the lever arm, �F is the force, and ×× denotes the cross product of two vectors.}

^{What is Angular Momentum?}

^{Angular momentum is a measure of how much an object rotates around an axis. It is also called the rotational momentum or the spin. Angular momentum is a vector quantity, which means it has both magnitude and direction. The magnitude of angular momentum depends on two factors:}

• ^{The moment of inertia of the object, which is a measure of how its mass is distributed around the axis of rotation}
• ^{The angular velocity of the object, which is a measure of how fast it rotates}

^{The direction of angular momentum is perpendicular to both the axis of rotation and the plane of rotation, and follows the right-hand rule: if you curl your fingers in the direction of rotation, your thumb will point in the direction of angular momentum.}

^{The formula for angular momentum is:}

^{�=��L=Iω}

^{where �L is angular momentum, �I is moment of inertia, and �ω is angular velocity.}

^{How are Torque and Angular Momentum Related?}

^{Torque and angular momentum are related by Newton’s second law for rotation, which states that:}

^{�=����τ=dtdL​}

^{where �τ is torque, �L is angular momentum, and �t is time.}

^{This equation means that torque is equal to the rate of change of angular momentum. In other words, torque causes angular momentum to change over time. If there is no net torque acting on an object, its angular momentum will remain constant. This is known as the conservation of angular momentum.}

^{The conservation of angular momentum explains many phenomena involving rotating objects, such as:}

• ^{Why a spinning top or a gyroscope stays upright even when tilted}
• ^{Why an ice skater can change their speed of rotation by changing their body position}
• ^{Why a planet orbits around a star in an elliptical path}
• ^{Why a black hole can have enormous angular momentum even though it has no size}

^Conclusion

^{Torque and angular momentum are two key concepts in physics that describe how forces affect rotating objects. Torque measures how much a force causes an object to rotate, while angular momentum measures how much an object rotates around an axis. Torque and angular momentum are related by Newton’s second law for rotation, which states that torque is equal to the rate of change of angular momentum. If there is no net torque acting on an object, its angular momentum will remain constant. This principle explains many phenomena involving spinning things in nature and technology.}