Impulse required to stop a rotating body

In summary, the conversation discussed the problem of determining whether a given torque vector will be enough to stop the rotation of a rigid body in 3D space over a given time step. The angular velocity and inertia tensor are known, so the angular momentum can be calculated. The goal is to stop the rotation without reversing it, and there was a discussion about using a component-wise comparison or scaling the other torque components accordingly. The concept of "center of percussion" was also mentioned as a way to stop the angular motion of a rigid body.
  • #1
cboyce
5
0
I have a rigid body rotating in 3D space. I have a torque vector that I want to apply to the rotating body over a given time step. What I want to know is, will the torque be enough to stop the body rotating on any of its axis and reverse direction, and, if so, exactly what would the torque vector be to stop the rotation instead of reverse it. The angular velocity is known, and the inertia tensor is known, so I am calculating the angular momentum as I * w.

The background to this is that I'm simulating the friction of a particular point on a body in space, and often times the torque created by the friction is more than adequate to stop the body from rotating, and if I apply the full friction-caused torque to the body, it actually rotates in the opposite direction, when what I really want to do is simply stop the rotation.
 
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  • #2
cboyce said:
if so, exactly what would the torque vector be to stop the rotation instead of reverse it.

Torque is the change of the angular momentum over time. If you know what change of angular momentum you want to achieve (to stop the rotation it is the negative of the current angular momentum) and the time period you want to apply the torque it rather trivial:
Torque = dL / dt
 
  • #3
Thanks for the reply. My problem is that I don't know how to determine if a given torque will stop the rotation over time. I understand how to find out the impulse to stop the rotation completely, but that's not what I necessarily want to do. I've got a torque that's working against the rotation, and at most, I want to stop the rotation rather than reverse it. I was thinking of doing a component-wise comparison, but I'm not sure if that's a valid approach. Basically, something like this:

I have an angular momentum of [1,2,3]. In order to stop the rotation in 1 second, I'd apply a torque of [-1,-2,-3]. But, the torque vector I want to apply is [0,-2,-4]. Would I be able to simply compare components and determine that the force I want to apply without reversing any rotational direction would be [0,-2,-3]?
 
  • #4
cboyce said:
I'm simulating the friction of a particular point on a body in space, [...] if I apply the full friction-caused torque to the body, it actually rotates in the opposite direction, when what I really want to do is simply stop the rotation.

I'm not sure I understand what your goal is. Possibly some information is missing

The whole idea of a simulation is that you set up the equations in such a way that blatantly unphysical outcomes are inherently impossible.

In the case of friction the quick 'n dirty approximation is to make the amount of friction proportional to the velocity. Then by the time the rotation has been reduced to zero the torque is down to zero.
 
  • #5
cboyce said:
I have an angular momentum of [1,2,3]. In order to stop the rotation in 1 second, I'd apply a torque of [-1,-2,-3]. But, the torque vector I want to apply is [0,-2,-4]. Would I be able to simply compare components and determine that the force I want to apply without reversing any rotational direction would be [0,-2,-3]?
I think that would be ok as an approximation, as long the time step is small.
 
  • #6
cboyce said:
I have an angular momentum of [1,2,3]. In order to stop the rotation in 1 second, I'd apply a torque of [-1,-2,-3]. But, the torque vector I want to apply is [0,-2,-4]. Would I be able to simply compare components and determine that the force I want to apply without reversing any rotational direction would be [0,-2,-3]?
On a second though: it would be better to scale the other torque components accordingly so you don't change its direction. In the above case you would apply [0,-1.5,-3]
 
  • #7
Look up "center of percussion" on google.
http://en.wikipedia.org/wiki/Center_of_percussion
An impulse (application of a force x time) applied at a single point can stop the the angular motion of a rigid body, but it will result in a linear motion of the center of gravity.
Bob S
 

1. What is impulse required to stop a rotating body?

The impulse required to stop a rotating body is the change in momentum needed to bring the body to a complete stop. It is a vector quantity with both magnitude and direction.

2. How is impulse related to rotational motion?

In rotational motion, the impulse required to stop a rotating body is equal to the change in angular momentum. This means that the greater the angular momentum of the body, the larger the impulse needed to stop it.

3. What factors affect the impulse required to stop a rotating body?

The factors that affect the impulse required to stop a rotating body include the mass, velocity, and distribution of mass of the body. A body with a larger mass or higher velocity will require a greater impulse to stop, while a more spread out mass distribution will require a smaller impulse.

4. Can the direction of the impulse affect the motion of a rotating body?

Yes, the direction of the impulse can affect the motion of a rotating body. The impulse can either be in the same direction as the motion of the body, which will increase its angular velocity, or in the opposite direction, which will decrease its angular velocity.

5. How is impulse calculated for a rotating body?

The impulse required to stop a rotating body can be calculated by multiplying the average torque applied to the body by the time interval in which it is applied. This can be represented by the equation J = τΔt, where J is the impulse, τ is the torque, and Δt is the time interval.

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