# Torque direction for any system of particles

• frozendemon
In summary, the problem involves a particle moving in an xy plane around the origin, with a given magnitude of angular momentum. The task is to find the torque acting on the particle at a specific time using the time derivative of the angular momentum. To determine the direction of the torque, the right hand rule can be used, with the direction being -k for clockwise rotation.

## Homework Statement

A particle is to move in an xy plane, clockwise around the origin as seen from the positive side of the z axis. In unit-vector notation, what torque acts on the particle at time t = 9.5 s if the magnitude of its angular momentum about the origin is (a) 8.0 kg·m2/s, (b) 8.0t^2 kg·m2/s3, (c) 8.0t^(1/2) kg·m2/s3/2, and (d) 8.0/t^2 kg·m2*s?

τ=dL/dt

## The Attempt at a Solution

All i have to do is take the time derivative of the given angular momentum and plug in t. I can get the magnitude of the torque with the equation but i do not know how to get the direction of torque. Please explain! Thanks

Look up the right hand rule :)

Well, I'm not too sure how to apply right hand rule with dl/dt, perhaps you can give me some insight?

Wait, do i just move my fingers to the direction its turning, in this case clockwise? If so then its -k, right?

I would like to clarify that torque is a vector quantity and therefore has both magnitude and direction. The direction of torque can be determined using the right-hand rule, which states that if you curl your fingers in the direction of rotation, the direction of your thumb will indicate the direction of the torque.

In this case, since the particle is moving clockwise around the origin, the direction of the torque will be in the negative z direction. This means that the torque vector will have components in the negative x and negative y directions, and can be expressed as (-τx, -τy, -τz) in unit-vector notation.

To determine the specific values for each component, you can use the given equations for the magnitude of angular momentum and take the time derivative to get the magnitude of torque. Then, using the right-hand rule, you can determine the direction of each component and express the torque vector in unit-vector notation.

I hope this explanation helps. Please let me know if you have any further questions.

## 1. What is torque direction and how is it determined for a system of particles?

Torque direction refers to the direction of rotation caused by a force acting on a system of particles. It is determined by the cross product of the force vector and the position vector from the axis of rotation to the point of application of the force.

## 2. How does the direction of torque affect rotational motion?

The direction of torque determines the direction of rotational motion. If the direction of torque is perpendicular to the axis of rotation, it will cause the system of particles to rotate. However, if the direction of torque is parallel to the axis of rotation, it will not cause any rotational motion.

## 3. Can the direction of torque change?

Yes, the direction of torque can change if the direction of the force or the position vector changes. Additionally, the direction of torque can also change if the axis of rotation is moved.

## 4. How do you calculate the direction of torque for a system of particles?

To calculate the direction of torque, you must first determine the cross product of the force vector and the position vector. The direction of the resulting vector will be perpendicular to both the force vector and the position vector and will indicate the direction of torque.

## 5. What are some real-life applications of understanding torque direction for a system of particles?

Understanding torque direction is crucial in many real-life applications, such as engineering and physics. For example, it is used in designing structures and machines to ensure they can withstand torque forces. It is also essential in sports, such as baseball, where understanding the direction of torque can help a player hit a ball with the desired spin. Additionally, torque direction is important in understanding the motion of celestial bodies in space.