The Role of Friction in Rotational Motion

[Rongeet Banerjee]

Homework Statement

A drum rolls down without slipping on an inclined plane.The frictional force:
1.converts translational energy to Rotational Energy
2.dissipates energy as heat
3.decreases Rotational motion
4.decreases both rotational and translational motion

Relevant Equations

Rotational Kinetic Energy= 1/2 *I*omega²
Translational Kinetic Energy= 1/2 *mv²

Friction provides the necessary torque for rolling without slipping.So Rotational Energy must increase.Simultaneously acceleration of centre of mass down the inclined plane is positive so Translational energy also must increase.Overall The Gravitational Potential Energy is getting converted to Kinetic Energy.Option 2 is the best option by my knowledge,but again my textbook contradicts my reason.It says option 1 is correct .Please explain

 

[DrClaude]

How is

Overall The Gravitational Potential Energy is getting converted to Kinetic Energy.

compatible with

2.dissipates energy as heat

?

 

[Rongeet Banerjee]

I meant that it was the Best Option.So how is translational energy getting converted to Rotational Energy.Aren't both of them increasing?

 

[Cutter Ketch]

I appreciate your distaste for option one. It isn’t really converting existing translational energy into rotational energy. Sometimes questions like these are frustratingly poorly worded. And that does leave you in a pretty bad pickle.

However, forgetting about the lack of a correct answer, let’s talk about why 2 is wrong. Picture a box resting on an inclined plane. Friction is keeping the box from sliding down the plane. The force of friction is there all day and all night for as long as you like. It can’t be imparting heat to the box because where would that energy come from? Static friction doesn’t impart heat, so if the drum doesn’t slip, no heat.

With the “correct” answer written in a way that it isn’t correct, I agree that in the real world 2 is often correct to some degree. Nothing real will move with absolutely no rubbing at that interface. But actually, you may have done physics experiments with things like hard steel balls and they came out pretty darn close to the behavior expected from energy conservation, right?

 

[Rongeet Banerjee]

I appreciate your distaste for option one. It isn’t really converting existing translational energy into rotational energy. Sometimes questions like these are frustratingly poorly worded. And that does leave you in a pretty bad pickle.

However, forgetting about the lack of a correct answer, let’s talk about why 2 is wrong. Picture a box resting on an inclined plane. Friction is keeping the box from sliding down the plane. The force of friction is there all day and all night for as long as you like. It can’t be imparting heat to the box because where would that energy come from? Static friction doesn’t impart heat, so if the drum doesn’t slip, no heat.

With the “correct” answer written in a way that it isn’t correct, I agree that in the real world 2 is often correct to some degree. Nothing real will move with absolutely no rubbing at that interface. But actually, you may have done physics experiments with things like hard steel balls and they came out pretty darn close to the behavior expected from energy conservation, right?

So how would you frame option1.Could you please explain your rhetoric in the last line because I have never performed that experiment.

 

[DrClaude]

I understand your and @Cutter Ketch's point, but I don't agree since for me the explanation below is reasonable.

So how would you frame option1.

In the absence of friction, to drum would slide down the inclined plane. Therefore it is the presence of friction that converts translational motion into rotational motion.

 

[jbriggs444]

From the point of view of translation, the tangential force of static friction up the slope acts to slow the cylinder, draining translational kinetic energy. It is acting opposite to the motion of the center of mass of the cylinder, doing negative [center-of-mass] work relative to the ground frame.

From the point of view of rotation, the tangential force of static friction up the slope acts to speed the rotation, adding rotational kinetic energy. It is acting in the same direction as the rotation, doing positive [real] work relative to a reference frame anchored at the center of mass.

The fact that the translation rate of the cylinder is increasing is due to gravity, not due to the resistance of static friction. Similarly, the fact that your car accelerates forward when the light turns green is due to the engine and tires, not due to rearward wind resistance.

 

[Cutter Ketch]

I understand your and @Cutter Ketch's point, but I don't agree since for me the explanation below is reasonable.

In the absence of friction, to drum would slide down the inclined plane. Therefore it is the presence of friction that converts translational motion into rotational motion.

You misquoted the answer. It said “ 1.converts translational Energy to Rotational Energy”. “Motion” is a fuzzy term that covers this notion of what might have been, but “Energy” is very specific.

It never had the translational energy that is in the rotational energy. How can it convert energy that doesn’t exist?!? If you want to put this in terms of rotational and translational energy the best you can say is “it causes gravitational potential energy that otherwise WOULD HAVE been converted to translational energy to instead be converted into rotational energy”. Yes, it is robbing energy that might have been translational, but it never went through actually being translational energy.

It absolutely does not convert translational energy into rotational energy. At no point is $\frac 1 2 mv^2$ reduced resulting in a commensurate increase in $\frac 1 2 I\omega ^2$

 

[jbriggs444]

If you want to put this in terms of rotational and translational energy the best you can say is “it causes gravitational potential energy that otherwise WOULD HAVE been converted to translational energy to instead be converted into rotational energy”.

That's just a quibble about book-keeping. But if you want to go there.

The correct book keeping is that gravitational potential energy goes into translational kinetic energy and that translational kinetic energy goes into rotational kinetic energy.

There is no gravitational torque and, accordingly, no path for gravitation to directly produce rotation.

 

[Rongeet Banerjee]

You misquoted the answer. It said “ 1.converts translational Energy to Rotational Energy”. “Motion” is a fuzzy term that covers this notion of what might have been, but “Energy” is very specific.

It never had the translational energy that is in the rotational energy. How can it convert energy that doesn’t exist?!? If you want to put this in terms of rotational and translational energy the best you can say is “it causes gravitational potential energy that otherwise WOULD HAVE been converted to translational energy to instead be converted into rotational energy”. Yes, it is robbing energy that might have been translational, but it never went through actually being translational energy.

It absolutely does not convert translational energy into rotational energy. At no point is $\frac 1 2 mv^2$ reduced resulting in a commensurate increase in $\frac 1 2 I\alpha ^2$

Nicely put forward.Really Understandable.Thank You very much.

 

[Cutter Ketch]

That's just a quibble about book-keeping. But if you want to go there.

The correct book keeping is that gravitational potential energy goes into translational kinetic energy and that translational kinetic energy goes into rotational kinetic energy.

There is no gravitational torque and, accordingly, no path for gravitation to directly produce rotation.

We can certainly disagree, but I really do disagree. The force does not increase the translational kinetic energy and then that translational kinetic energy reduced at the expense of increasing rotational kinetic energy. It doesn’t happen. If you throw a ball and it hits the floor friction reduces 1/2 mv^2 and increase 1/2 I w^2. (Oops! I just this moment realized in my concentrating on proper Latex I accidentally wrote alpha where I meant omega in a previous pot). Now that is converting translational energy into rotational energy. Here friction robs the force before the work is ever done. Every bit of F d goes into translational kinetic energy it never got any more, and it never lost any. Friction made F smaller, but that isn’t energy!

 

[haruspex]

There is no gravitational torque

Depends on choice of axis. Consider point of contact.

The correct book keeping is that gravitational potential energy goes into translational kinetic energy and that translational kinetic energy goes into rotational kinetic energy.

I cannot see how that is the correct bookkeeping. It is at least as arguable, even rather more so, that GPE goes into both at once.