Torque and angular momentum for a Particle in a Force Field

In summary, the conversation discusses finding the torque and angular momentum for a particle in a force field with a given equation at a specific time. The proper method is to equate r" to F and then take the cross product of r and F. It is important to consider initial conditions for both r and r'.
  • #1
so09er
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[SOLVED] Torque and angular momentum for a Particle in a Force Field

Find A) the torque and B) the angular momentum about the origin at the time t=3 for a particle in a Force Field F=(3t^2 -4t)i + (12t -6)j + (6t - 12t^2)k. Assuming that t=0 is located at the origin.


I equated r"=F then took r X F is this the proper way? Then took r X v to find angular momentum. Any help would be appreciated.
 
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  • #2
Yes, that's the right way. Solve the differential equation r''=F and find v and r at t=3. You not only need to assume r(0)=(0,0,0), you need some initial condition for r'(0). Is it also (0,0,0)?
 
  • #3
Thanks for the confirmation
 

What is torque?

Torque is a measure of the rotational force applied to an object. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation.

What is angular momentum?

Angular momentum is a measure of an object's rotational motion. It is calculated by multiplying an object's moment of inertia (a measure of its resistance to rotational motion) by its angular velocity (how fast it is rotating).

How is torque related to angular momentum?

Torque and angular momentum are directly related, with torque being the cause of changes in angular momentum. When torque is applied to an object, it can change its angular momentum by either speeding up or slowing down its rotation.

What is a force field?

A force field is a region in space where objects experience a force. It can be visualized as a map of vectors that show the direction and magnitude of the force at different points in the field.

How do torque and angular momentum apply to a particle in a force field?

When a particle is in a force field, it experiences a force that can cause it to rotate. This rotation creates torque, which can change the particle's angular momentum. The particle will continue to rotate and its angular momentum will remain constant unless acted upon by an external torque.

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