Why Objects Rotate: Rigidity, KE & Magnets

[Gurdian]

Just from the most basic concepts, is it due because of rigidity that when a force is applied to a non COM point that an object rotates? Why does the magnitude of rotation increase with increased perpendicular distance from the pivot or COM point.

Also do you transfer more KE to an object when you give it both linear and angular rotation?

Please use N1, 2 or 3 only, if possible.

P.S I'm also meant to understand how this induces EM waves when using magnets, but I don't really have an issue with that, thanks.

 

[Simon Bridge]

Objects rotate wen there is a net central force on each of the components, in conjunction with a tangential speed.

The internal forces between each of the components (atoms, molecules, whatever) usually provide the centripetal force, the external force provides the tangential velocity - I take it you have no problem with a tether-ball rotating?
Your intuition to do with rigidity is a good one but even non-rigid bodies may rotate - like liquids or gasses.

When you set an object spinning, you have to do some work - this energy is stored in the rotation.
Energy stored in this way can be thought of as a form of kinetic energy and is in addition to any translational kinetic energy the object may have.

I don't know what you mean by N1,2 or 3.

I don't know what you mean by "magnitude of rotation".
An object rotates through an angle - it is the same angle no matter what the radius of the object is.
The angular velocity need not increase with radius either - eg. outer planets have slower angular speeds than the inner ones.

 

[Andrew Mason]

Just from the most basic concepts, is it due because of rigidity that when a force is applied to a non COM point that an object rotates? Why does the magnitude of rotation increase with increased perpendicular distance from the pivot or COM point.

Also do you transfer more KE to an object when you give it both linear and angular rotation?

Please use N1, 2 or 3 only, if possible.

P.S I'm also meant to understand how this induces EM waves when using magnets, but I don't really have an issue with that, thanks.

If a force is applied to a body at a distance from the centre of mass (com) but not directed toward the com, there is a torque about the com. Torque is equal to the time rate of change of angular momentum, L = Iω. So L changes. Since I is constant, this means ω, the angular speed of the body about the centre of mass must change. That is basically it.

AM

 

[voko]

Objects can rotate without any external force applied to them.

Far more important for rotation are internal forces. Without internal forces, nothing would rotate. Everything would just go in every possible direction, straight. This is Newton's first law.

 

[Gurdian]

Objects rotate wen there is a net central force on each of the components, in conjunction with a tangential speed.

The internal forces between each of the components (atoms, molecules, whatever) usually provide the centripetal force, the external force provides the tangential velocity - I take it you have no problem with a tether-ball rotating?
Your intuition to do with rigidity is a good one but even non-rigid bodies may rotate - like liquids or gasses.

When you set an object spinning, you have to do some work - this energy is stored in the rotation.
Energy stored in this way can be thought of as a form of kinetic energy and is in addition to any translational kinetic energy the object may have.

I don't know what you mean by N1,2 or 3.

I don't know what you mean by "magnitude of rotation".
An object rotates through an angle - it is the same angle no matter what the radius of the object is.
The angular velocity need not increase with radius either - eg. outer planets have slower angular speeds than the inner ones.

Sorry by n1, 2 and 3 I meant Newtons three laws of motion. By magnitude of rotation I meant moment, understanding why the mokent increases would be great

Kinetic energy is stored in rotation? Like some sort of stationary wave or something?

Is orbiting a kind of rotation?

If a force is applied to a body at a distance from the centre of mass (com) but not directed toward the com, there is a torque about the com. Torque is equal to the time rate of change of angular momentum, L = Iω. So L changes. Since I is constant, this means ω, the angular speed of the body about the centre of mass must change. That is basically it.

AM

Thanks but I already know whay torque means, it's a rate of change of angular momentum, I just wanted to know what causes it. Also why it is larger with increased distance from the com or axis of rotation or COM.

Objects can rotate without any external force applied to them.

Far more important for rotation are internal forces. Without internal forces, nothing would rotate. Everything would just go in every possible direction, straight. This is Newton's first law.

When you say objects can rotate without external pulses do you mean it can rotate indefinitely in a vacuum after an impulse?

What you said about internal forces has helped me understand why the rotate I take it the internal forces oppose the motion of one of the molecules within the object and this opposition extends throughout the object but sometimes to a greater extent in rigid bodies (or all the time)?

Also why does torque increase with increased distance from the com, I know it should be intuitive upon learning that the torque is first set up when a non com point is acted upon by a force, but why isn't the torque constant for any point acted upon? I know there is a larger change in angular momentum (moment of inertia • mass) for a given time, what I'm asking then is why does I (moment of inertia) increase with radius.

Thanks for answering why objects rotate.

 

[A.T.]

I know it should be intuitive upon learning that the torque is first set up when a non com point is acted upon by a force, but why isn't the torque constant for any point acted upon?

That would be an ugly discontinuity in nature, if the torque would jump from zero to some large constant value, just because the force is moved by an arbitrary small distance off COM.

See also older threads about the question, how static linear forces lead to the concept of torque. For example post #3 & #10 here:
https://www.physicsforums.com/showthread.php?p=4486117

I'm asking then is why does I (moment of inertia) increase with radius.

That follows from geometry and linear inertia. More radius -> more linear (tangential) acceleration for the same angular acceleration.

 

[Gurdian]

That would be an ugly discontinuity in nature, if the torque would jump from zero to some large constant value, just because the force is moved by an arbitrary small distance off COM.

See also older threads about the question, how linear forces lead to the concept of torque. For example post #3 & #10 here:
https://www.physicsforums.com/showthread.php?p=4486117

That does sound ugly, I'll check out that thread thanks.

 

[Andrew Mason]

Thanks but I already know whay torque means, it's a rate of change of angular momentum, I just wanted to know what causes it. Also why it is larger with increased distance from the com or axis of rotation or COM.

Torque increases with distance from the com because of the way torque is defined: τ = F x r. A force acting at a distance r from the com causes a torque about the com whose magnitude is Frsinθ where θ is the angle between the direction of the force at the point of application and the vector from that point to the centre of mass. Torque is measured relative to the centre of rotation, which is the com for a free rigid body.

When you say objects can rotate without external pulses do you mean it can rotate indefinitely in a vacuum after an impulse?

A rotating free body will continue to rotate at the same angular speed unless its moment of inertia changes or unless a torque is applied to it. That is evident from: L/I = ω

AM

 

[Gurdian]

Torque increases with distance from the com because of the way torque is defined: τ = F x r. A force acting at a distance r from the com causes a torque about the com whose magnitude is Frsinθ where θ is the angle between the direction of the force at the point of application and the vector from that point to the centre of mass. Torque is always measured relative to the centre of rotation, which is the com for a free rigid body.

A rotating free body will continue to rotate at the same angular speed unless its moment of inertia changes or unless a torque is applied to it. That is evident from: L/I = ω

AM

Someone derived the equation for moment of inertia using KE but it didn't look right it was [integrate] r^2 dm where m is mass, that didn't look right to me because I thought "I" was r^2*m.

Any I took a look at the threead suggeted as well as the explanations and they were too elaborate as I requested in the OP I just wanted to know it from basic principles.

If the point is further away from the radius less force is required to cause rotation because torque = rF.

Rotation is a result of the internal forces but it seems as if the internal forces that act againts the external force isn't equal about the point of action if the point if the point is a non com point.

So is it a case of the further you are from the center the less balanced the opposition is to the removal of the molecule is?

That wouldn't explain why "I" = r^2 * m.

Maybe I didn't understand the integration.

( total KE of rotation) T = (1/2)(w^2) int (r^2) dm = (1/2)(w^2) I, Where I = int (r^2) dm.

 

[voko]

What you said about internal forces has helped me understand why the rotate I take it the internal forces oppose the motion of one of the molecules within the object and this opposition extends throughout the object but sometimes to a greater extent in rigid bodies (or all the time)?

I am struggling to understand what is being said here. Let's take the simplest example of a body: two particles that are very strongly attracted to each other. If you push one of them perpendicularly to the line of attraction with the other one, then by Newton's first law it will try to move along the direction of its velocity. The attractive force, however, does not let that happen. It pulls the "break-away" particle in, changing the direction of its velocity. By Newton's third law, the attractive force also pulls the other other particle in the opposite direction. They begin revolving about their center of mass. The attractive force cannot change the magnitude of velocity, because it is always at the right angle with the velocity, so the situation continues indefinitely (unless there is some external force such as friction). This is rotation.

 

[Gurdian]

I am struggling to understand what is being said here. Let's take the simplest example of a body: two particles that are very strongly attracted to each other. If you push one of them perpendicularly to the line of attraction with the other one, then by Newton's first law it will try to move along the direction of its velocity. The attractive force, however, does not let that happen. It pulls the "break-away" particle in, changing the direction of its velocity. By Newton's third law, the attractive force also pulls the other other particle in the opposite direction. They begin revolving about their center of mass. The attractive force cannot change the magnitude of velocity, because it is always at the right angle with the velocity, so the situation continues indefinitely (unless there is some external force such as friction). This is rotation.

I didn't think of using a simple molecule to illustrate it, just large systems.

So when I push one atom it accelerates during the application of the force, all the while attraction of the other atom opposes this by pulling the break away atom toward it and due to N.3rd the break away molecule does that same.

Is this what simon bridge meant by the KE being conserved?

 

[voko]

I do not think he meant KE is conserved. What he meant is that some KE is always there when things are in motion, and rotation is a motion. If a perfectly rigid body rotating in some environment with resistance, yes, KE is conserved. In semi-rigid bodies, such as, for example, the Sun-Earth pair, there are some tiny fluctuations of the distance between the constituent parts, and KE fluctuates as well, Total energy, which is KE + PE of the interaction, is conserved.

 

[Gurdian]

I do not think he meant KE is conserved. What he meant is that some KE is always there when things are in motion, and rotation is a motion. If a perfectly rigid body rotating in some environment with resistance, yes, KE is conserved. In semi-rigid bodies, such as, for example, the Sun-Earth pair, there are some tiny fluctuations of the distance between the constituent parts, and KE fluctuates as well, Total energy, which is KE + PE of the interaction, is conserved.

Right I see, and for torque whe torque increases with distance from the center, what does that mean and why does it happen? Are more molecules pulling I the direction of rotation when r is larger? I really don't understand the moment of inertia and where it comes from.

 

[voko]

For the object to rotate as a whole, its outer parts must be moving faster than its inner parts. Greater velocity at the periphery means greater energy required to spin it up, greater force (torque) to alter its rotation. The moment of inertia is a quantitative measure of rotational inertia, just like the term suggests.

 

[Gurdian]

For the object to rotate as a whole, its outer parts must be moving faster than its inner parts. Greater velocity at the periphery means greater energy required to spin it up, greater force (torque) to alter its rotation. The moment of inertia is a quantitative measure of rotational inertia, just like the term suggests.

But I don't understand, that's what I thought until I read that the larger the distance the less force required for amoment of equal magnitude.

Why is it easier to achieve the same rotation if you apply the force further away from the pivot?

Or is it a case of for any given force (change in monetum over change in time) the required torque required for the same rotation to occur in larger with a greater distance from the pivot? Since T = rF?

Also since all points rotate isn't the same KE transferred irrespective of where the force is applied?

 

[voko]

These are two different things. One is the inertia of rotation. The "bigger" the body is, the greater it is.

Another is the torque. The farther a force is applied from the axis of rotation, the greater the it is.

 

[Gurdian]

These are two different things. One is the inertia of rotation. The "bigger" the body is, the greater it is.

Another is the torque. The farther a force is applied from the axis of rotation, the greater the it is.

Right I understand the moment of inertia now, and why things rotate (to the level that is necessary for me to continue reading) what I don't understand is why the torque is larger for a greater distance from the pivot, is it that a larger torque is required for a given magnitude of angular displacement or is a larger torque produced for a given magnitude of angular displacement.

So F = (p)/t, rF by definition = torque, by multiplying both sides by r we get the formula for angular moment L.

Now I take it this means that if you apply a force F a at great distance from the pivot you produce a large torque, change in angular moment over time, but if the body is rigid isn't the change in angular momentum going to be the same, in each case? Why does applying a force far away from the pivot point produce a larger torque or require one.

Why is the moment larger with distance from tbe pivot point?

I'm seriously confused by rotating objects getting past this will be awesome, thanks.

 

[voko]

Do you understand levers? They also work due to the properties of torque.

 

[Gurdian]

Do you understand levers? They also work due to the properties of torque.

You pull the lever with a small amount of force but the torque generated is large because of the distance from the pivot, and that large torque is used to rotate something smaller that would have required a large forcec to turn?

 

[voko]

Yeah, this is something known as the "mechanical advantage". Or the "golden rule of mechanics". Look it up.

 

[Gurdian]

Yeah, this is something known as the "mechanical advantage". Or the "golden rule of mechanics". Look it up.

So torque is just the capacity to cause rotation? I thought it meant that rotation of the object was made easier.

May I ask a question.

Why is it that if I have a light plank on a seesaw and I put a particle on either side of the pivot, each of equal mass, the
particle that is farthest from the pivot, actually I think I understand now.

The angular momentum of the rotation about the pivot is greater for the half of the pivot that is supporting the paritcle at a greater distance from the pivot.

Btw for a free object, does it rotation about the axis of rotation becuse the axis of rotation is a point that can not rotate about any part of that same object.

 

[voko]

Yes, torque is the capacity to cause rotation, or, more precisely, to alter the state of rotation. Moment of inertia is the capacity to resist the alternation of rotation. So these are complimentary, exactly as mass and force.

 

[Gurdian]

One last question if I had a uniform line of atoms bonded and I applied a force at one end cold you go through how that line of atoms bonded would respond so that a rotation would occur.

Everything should be cleared up after that.

 

[voko]

It is not much different from a pair of atoms. Atom one is being nudged. It is attracted to atom two, so the two are set into mutual rotary motion as described earlier... and now atom two is to atom three as atom one is to atom two. And so on.

Well, it is a little more complex than that, but the general idea is right.

 

[Gurdian]

It is not much different from a pair of atoms. Atom one is being nudged. It is attracted to atom two, so the two are set into mutual rotary motion as described earlier... and now atom two is to atom three as atom one is to atom two. And so on.

Well, it is a little more complex than that, but the general idea is right.

Ok that's what I thought.

Thanks for clearing things up.

 

[jbriggs444]

One last question if I had a uniform line of atoms bonded and I applied a force at one end cold you go through how that line of atoms bonded would respond so that a rotation would occur.

If I understand this question correctly, you are asking about something like a long stick that is shoved sideways at one end. So you are not talking about a compression or tension force being propagated from one end to the other. You are asking about an explanation for the shear force.

An analogy may help. Think about a truss bridge. You have girders running to form little triangles all along the length of the truss. These girders and their joints to one another are strong in tension and compression. The girders need not be strong against bending. The joints between the girders do not need to be very strong against angular forces.

The shear stresses that are present in the large can be resisted by nothing but tension and compression in the small.

 

[Simon Bridge]

So torque is just the capacity to cause rotation? I thought it meant that rotation of the object was made easier.

May I ask a question.

Why is it that if I have a light plank on a seesaw and I put a particle on either side of the pivot, each of equal mass, the
particle that is farthest from the pivot, actually I think I understand now.

:D

One of the useful things about explaining what you don't understand is that, if you do it right, understanding dawns.
The see-saw thing is just geometry in action.

Btw for a free object, does it rotation about the axis of rotation becuse the axis of rotation is a point that can not rotate about any part of that same object.

The axis of rotation has to be a line through the center of mass for that kind of reason, yes.
But not that exact reason.

We divide the general motion of the object into motion of the center of mass (translation) and change in orientation about the center of mass (rotation) because it turns out to be convenient - it makes the math simpler.
The effect comes from geometry like with the see-saw.
If you feel you have the math, have a look at http://home.comcast.net/~szemengtan/ on Classical Mechanics,
Ch2: http://home.comcast.net/~szemengtan/ClassicalMechanics/SystemsAndRigidBodies.pdf (s3 on p5) is the bit you want.
But if you are just starting out - this will probably be overkill.

TLDR: To get the center of mass to go in a circle requires an external force to the object.

Things to try:

Make a top (a 5cm radius circle of stiff card with a pencil rammed trough it say) that spins nicely - then add a (very) small weight to the edge, in just one spot - a paperclip will do. Watch carefully and you should see how this works. If you spin it through the air - how does it fly compared to the case without the extra mass?

Not all possible lines through the center of mass are equivalent though. You can practice by trying out different ways of spinning a brick - preferably one where the length, width, and depth are different sizes.

You should be able to get it to spin about the longest or the shortest axis - but trying the middle axis will get you very complicated motion. This is because there is more going on that what you have learned so far.

When you start out learning about rotational motion, you are dealing only with quite simple situations. This is so you can learn the math without getting bogged down in details. At the level you appear to be on it is a matter of making definitions - and the rest is geometry. There's a certain amount you end up taking on trust - just to get through the exam.

You are well advised to construct simple experiments like I suggested above to get used to how things work.
It's an essential part of understanding physics.