Torque direction for any system of particles

[frozendemon]

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?

Homework Equations

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

 

[JHamm]

Look up the right hand rule :)

 

[frozendemon]

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

 

[frozendemon]

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

 

[asteriatic]

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.