# Torque on Stick

1. Jan 25, 2010

### Biggidy

1. The problem statement, all variables and given/known data

A stick is held by one end and swung in an arc and released at the horizontal. About which point will it rotate before hitting the ground?

2. Relevant equations

Torque on an object = l (length from incidence of torque) x force

3. The attempt at a solution

There is no longer any force on the object, so I think it should rotate either around the middle or one of two ends.
Would it rotate about the middle of the stick, point at which it was held, or point farthest away?

Thanks

Last edited: Jan 25, 2010
2. Jan 25, 2010

### pgardn

When you were holding the stick, its axis of rotation had to be through your hand as you basically stated. If you pushed a stick in space at some distance away from the center of mass and then stopped pushing, about what point on the stick would the rotation occur?

If you push any object at some distance away from the center of mass, about which point will the object rotate after the force is zero?

3. Jan 25, 2010

### Biggidy

Would it rotate about the furthest point from the center of mass?

I'm sorry, I don't understand the push reference.

Could anyone clear this up?

Last edited: Jan 25, 2010
4. Jan 25, 2010

### pgardn

A push is a force. If the force is applied at some distance from the axis of rotation of an object that is called torque. If an object is not restricted by a rod, pin or something else that makes the object rotate around that pin or rod or whatever, then what will it rotate about?

That is why I asked about an object out in space. In space we presume the object would not be under any influence other than a push (force) you might give it. And if you do push it some distance away from its center of mass, like at the end of the rod but lets say perpendicular to the rod it will rotate about what?

I would now grab a pencil by the end and fling it across the room. Do both ends rotate, or only one end? If both ends rotate then it is not rotating about an end.

5. Jan 25, 2010

### Biggidy

Oh, so the force is acting at the held point. And this causes it to rotate about the furthest end, away from the force that was applied?

6. Jan 25, 2010

### pgardn

Did you fling the pencil?

Try it this way. Hold the pencil at one end with the other end sticking straight up. Then fling the pencil. As it falls to the ground are both ends rotating or only one end? If both ends are rotating, what does it tell you about the place on the pencil about which it rotates?

7. Jan 25, 2010

### Biggidy

Yes. It rotated end over end, so this makes me think that it rotates about the farthest end of the point at which is it held.

Sorry: EDIT

It rotated about the furthest point, but this doesn't make sense to me, because it seems like the force should propel the point at which you hold over the furthest end.

Help?! Very confused.

Last edited: Jan 25, 2010
8. Jan 25, 2010

### pgardn

If both ends of the penci were rotating then the pencil was rotating around some point in the middle. The center of mass.

I was just trying to get you to understand many things that rotate do so about their center of mass if they do not have a fixed rotation point to supply a normal force. For example, if you stuck a pencil through a paper plate but not through the center, and then twirled the pencil to give the plate rotation, it would rotate about the pencil but not its center of mass.

Back to the original question. Lets say a string was attached to one end of the pencil and you then grabbed the string a twirled the pencil in a vertical circle. And then let go of the string exactly when the pencil was horizontal on its way up, or horizontal on its way down...

The string would be supplying centripetal force keeping the pencil moving in an arc until you let go of the string. The furthest piece of the pencil from the string would actually have a larger centripetal force applied to it because it is moving faster even though is r (radius is larger). When you let go the furthest piece of the pencil will be moving faster than the part of the pencil where the string is tied.
Does this make sense?

9. Jan 25, 2010

### Biggidy

Yes!

That makes sense according to my knowledge of the equation of centripetal equaling v to the power of 2/radius. Therefore, if you increase the distance (ie. the farthest point of the pencil), it will have more centripetal acceleration, therefore, the pencil will spin about the point at which it was held!

Right!?

10. Jan 25, 2010

### pgardn

Darn it... I interjected some side stuff and messed you up.

Lets say the pencil was a disc. Like a record. If you let go of the string, the part of the record furthest from the string would be moving faster than the part of the record attached to the string as you were swinging the record in a vertical loop. When you let go of the string the record would rotate about the center would it not?

Same with all my pencil examples. Flinging, swinging in a circle in each case one part of the pencil has a higher linear velocity than the other part so it rotates when you let go. If you hit the end of a pencil with your finger as it was not rotating up in the air it would begin to rotate because you gave it some torque. But after that torque was applied and you were no longer flicking the pencil with your finger it would rotate about its center of mass. And keep rotating until some other torque stopped it from doing so. Like hitting the ground.

Sorry I messed you up.

11. Jan 25, 2010

### Biggidy

Okay, so let me get this straight, it would rotate around its center of mass, and not about the point at which it was held?

Thanks

12. Jan 26, 2010

### pgardn

Yes.

Think about a pencil thrown up in the air rotating about one of its ends. What would keep that end from rotating? Think about a diver on a spring board and how odd it would look if when in an erect position, the diver rotated about his feet or head...