Torque and Angular Momentum §

Introduction §

In the realm of physics, particularly when discussing rotational motion, two fundamental concepts emerge: torque and angular momentum. These concepts are pivotal in understanding how objects rotate and maintain their motion.

Torque §

Definition §

Torque, often symbolized as $\tau$, is a measure of the force causing an object to rotate. Mathematically, torque is defined as:

$\tau =r\times F$

Where:

• $r$ is the position vector (distance from the pivot point to the point where force is applied),
• $F$ is the force applied,
• $\times$ represents the cross product.

Significance §

Torque is crucial in determining how an object starts rotating, changes its rotational speed, or comes to a stop. It’s the rotational equivalent of linear force.

Angular Momentum §

Definition §

Angular momentum, represented as $L$, is the rotational equivalent of linear momentum. It is defined as the product of the moment of inertia $I$ and angular velocity $\omega$:

$L=I\omega$

Where:

• $I$ is the moment of inertia, a measure of an object’s resistance to changes in its rotation,
• $\omega$ is the angular velocity.

Conservation §

The principle of conservation of angular momentum states that if no external torque acts on a system, the total angular momentum of the system remains constant.

Relationship Between Torque and Angular Momentum §

The relationship between torque and angular momentum is governed by the equation:

$\tau =\frac{dL}{dt}$

This equation implies that the torque applied on an object is equal to the rate of change of its angular momentum.

Examples in Daily Life §

1. Bicycle Wheels: The stability of a bicycle at speed is a result of angular momentum.
2. Gymnastics: Gymnasts use the principles of angular momentum and torque to control their motion during flips and spins.

Conclusion §

Understanding torque and angular momentum provides insight into the dynamics of rotational motion, which is a fundamental aspect of many physical systems.

Test Questions §

1. STARTI [Basic] Question: What is the formula for torque? Back: The formula for torque is $\tau =r\times F$, where $r$ is the position vector, and $F$ is the force applied. ENDI
2. STARTI [Basic] Question: Explain the conservation of angular momentum. Back: The conservation of angular momentum states that if no external torque acts on a system, the total angular momentum of the system remains constant. ENDI
3. STARTI [Basic] Question: How is torque related to the change in angular momentum? Back: Torque is related to the change in angular momentum by the equation $\tau =\frac{dL}{dt}$, meaning the torque applied is equal to the rate of change of angular momentum. ENDI