Rotation Mechanics about Unfixed Points

In summary, this question is asking about how to find the speed of translation and rotation of a floating object depending on where along the object an impulse is applied. The person is not sure how to find the speeds, but thinks that it may be related to torque and angular momentum.
  • #1
jchodak2
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I was doing some rotation problems the other day out of my physics textbook when I realized that invariably all the problems dealt with rotation about fixed point (levers and pendulums and such). So I imagined a case in which I had a bar with a certain mass and dimension floating in space and I applied an impulse at some point on the bar (shot a bullet or a piece of gum, ellastic or inellastic, whatever), and I wanted to know how fast the bar would begin to translate compared to how fast it would rotate depending on where along the bar I applied the impulse (obvioulsy if I shot at it dead center it would translate only). I wasn't sure how to work this out and how I would employ the relevant kinematic equations for translation and rotation and linear vs angular momentum. This seems like an easy enough and straightforward problem, but I couldn't work it out and I found it interesting that my book had absolutely no problems of this kind. Can anyone help me?
 
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  • #2
This is a very interesting question. The first thing is that momentum is conserved so momentum of object doing the impulse = angular + translational.

Next thing is perhaps to figure out the moment of inertia and the length of the bar and then you'd be able to solve for one of the velocities from which you could figure out the other
 
  • #3
Not pretending to be an expert, but I think this may be relevant.

When dealing with torque, there is general agreement that the magnitude of the torque is equal to the distance from the center of mass to the action point multiplied by the force component perpendicular to this line, or [tex]\vec{\tau}=\vec{r}\times \vec{F}[/tex]. This is the part of the force contributing to rotational motion, so the component of the force parallel to [tex]\vec{r}[/tex] must contribute to translateral motion, right?

I haven't studied collisions that closely yet, but I should think that there is a similar way to deal with collision situation, though you will have to include conservation of angular and linear momentum.
 

FAQ: Rotation Mechanics about Unfixed Points

1. What is rotation mechanics about unfixed points?

Rotation mechanics about unfixed points is a branch of physics that deals with the study of rotational motion of objects around a point that is not fixed or stationary. It involves understanding the forces and dynamics involved in objects rotating around a point that is subject to change.

2. How is rotation about unfixed points different from rotation about fixed points?

Rotation about unfixed points differs from rotation about fixed points in that the point of rotation is not stationary or fixed. This means that the forces and dynamics involved in the rotation are constantly changing, making the motion more complex and difficult to predict.

3. What are some real-world examples of rotation mechanics about unfixed points?

Some real-world examples of rotation mechanics about unfixed points include the motion of a spinning top, the rotation of planets and moons around a changing axis, and the rotation of a helicopter blade around its rotor axis.

4. What principles and laws govern rotation mechanics about unfixed points?

The principles and laws that govern rotation mechanics about unfixed points include torque, angular momentum, conservation of angular momentum, and the law of inertia. These laws help to explain the motion and dynamics of objects rotating around a changing point.

5. Why is the study of rotation mechanics about unfixed points important?

The study of rotation mechanics about unfixed points is important because it helps us understand the complex motion of objects in the natural world. It also has practical applications in engineering, such as in the design of gyroscopic systems, helicopters, and other rotating machinery.

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