Torque and Angular Momentum : Explain

1. Torque:

Torque is a force that causes something to rotate around an axis. You can think of it like a “twist” or “turning force.”

Imagine this:

If you try to open a door, you’re applying a force to the door’s handle. But, the force isn’t just pushing straight forward—you’re pushing sideways at the handle to make the door rotate around its hinges.
Torque is the measure of how much that force is trying to rotate the door.

Mathematically, torque (

$tau$

) is calculated as:

tau = F times r times sin(theta)

Where:

$F$

is the force applied (like pushing on the door).
$r$

is the distance from the axis of rotation (like the distance from the door’s hinges to where you push).
$theta$

is the angle between the force and the line connecting the point of force to the axis of rotation (usually the door’s hinges).

Key Points:

More torque is generated if the force is applied farther from the axis (the handle of the door).
The greater the force and the farther it’s applied from the center, the more torque it creates.
If you push at an angle, only the component of the force that is perpendicular to the line connecting the force point to the axis will create torque.

Everyday example:

Opening a door: When you push near the edge of the door (far from the hinges), it’s easier to open because you’re creating more torque. If you push near the hinges (closer to the axis), it’s harder because the torque is smaller.

2. Angular Momentum:

Angular Momentum is a measure of how much motion something has when it’s rotating. Just like how momentum describes how much motion a moving object has in a straight line, angular momentum describes rotational motion.

Imagine this:

Think of a figure skater spinning. When the skater pulls in their arms, they spin faster, and when they extend their arms, they slow down. The angular momentum stays the same (unless something external acts on the skater), but the speed of spinning changes based on how the mass is distributed.

Angular momentum (

$L$

) is calculated as:

L = I times omega

Where:

$I$

is the moment of inertia (which tells you how difficult it is to rotate an object).
$omega$

is the angular velocity (how fast the object is rotating).

Key Points:

Angular momentum depends on both how fast an object is spinning and how its mass is distributed.
If an object is rotating faster or has more mass further from the axis of rotation, it has more angular momentum.

Conservation of Angular Momentum:

One important principle is that angular momentum is conserved if no external torque is acting on the object. This means if a rotating object’s shape changes (like a skater pulling in their arms), its speed of rotation will change to keep the total angular momentum constant.

Everyday example:

Figure Skater: When the skater pulls in their arms, they rotate faster, but their angular momentum stays the same. When they extend their arms, they slow down because their moment of inertia increases, and to keep angular momentum constant, their angular velocity (speed of rotation) decreases.

Summary:

Torque: A twisting force that causes an object to rotate. It depends on how much force is applied and how far from the rotation axis the force is.
Angular Momentum: A measure of how much rotational motion an object has, depending on how fast it’s spinning and how its mass is distributed. It stays constant unless something acts on the object to change it.

In simple terms:

Torque is what gets an object spinning.
Angular Momentum is how much spinning the object has once it’s moving.

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