# Torque and angular momentum with a central force

• fer Mnaj
In summary, torque is the force that causes an object to rotate around an axis, while angular momentum is the measure of an object's tendency to keep rotating at a constant rate. A central force is one that acts towards or away from a central point, and is important in understanding the motion of objects with rotational symmetry. Torque and angular momentum are closely related, with a change in one resulting in a change in the other. The equations for torque and angular momentum are T = r x F and L = Iω, respectively. Central forces can affect the motion of objects by changing the direction of their angular momentum, either by changing the direction of rotation or the speed and direction of rotation.
fer Mnaj
Homework Statement
Consider the central force ##F (r) = - k / r^2 ˆr ## to which a particle of mass m is subject; where ˆr is the unit vector along the line connecting the center of forces with the position of the particle. Calculate the torque that F exerts on m and the angular momentum of the particle;
Calculate the torque that F exerts on m and the angular momentum of the particle;
both quantities with respect to O
Relevant Equations
τ= r x F L=rxp
HI

τ= r ˆr x - ##k / r ^ 2## ˆr= 0 right? since ˆr x ˆr is zero

#### Attachments

• Central force.png
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As you say, ##\vec L = \vec r \times \vec p ## . If you have no further information, that's it.

## 1. What is torque and angular momentum?

Torque is the measure of the force that causes an object to rotate around an axis. Angular momentum is the measure of an object's rotational motion, taking into account its mass, velocity, and distance from the axis of rotation.

## 2. What is a central force?

A central force is a type of force that acts towards or away from a fixed point, known as the center of force. This type of force only depends on the distance between the object and the center of force, and not on the direction of the object's motion.

## 3. How is torque related to central force?

Torque is directly proportional to the central force and the distance between the object and the center of force. This means that as the central force or the distance increases, so does the torque.

## 4. How does angular momentum change with a central force?

When a central force acts on an object, it causes a change in the object's direction of motion, thus changing its angular momentum. If the force is directed towards the center, the object will experience an increase in angular momentum, and if the force is directed away from the center, the object will experience a decrease in angular momentum.

## 5. What are some real-world applications of torque and angular momentum with a central force?

Some examples of real-world applications of torque and angular momentum with a central force include the motion of planets around the sun, the rotation of a spinning top, and the movement of a bicycle wheel. These principles also play a crucial role in the design and functioning of machines and engines.

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