How Does Friction Affect Energy Conservation in Rolling Motion?

[konichiwa2x]

Hi,

I got a doubt while studying rotational mechanics. It is said in my book that when a sphere is purely rolling on a surface, total mechanical energy is conserved even though friction is acting. Isnt friction an external force? How can energy be conserved then??

Another doubt I got is the following: I understand that it is the torque due to friction that helps a body roll. Hence, friction actualy helps motion.. Then why does the rolling body ever come to stop??

Please help me get this cleared. thanks for your time.

 

[Doc Al]

It is said in my book that when a sphere is purely rolling on a surface, total mechanical energy is conserved even though friction is acting. Isnt friction an external force? How can energy be conserved then??

Yes, friction is an external force. But as long as there is no slipping, the static friction does no work and thus does not affect the mechanical energy.

Note that when the sphere is rolling along a horizontal surface, the static friction is zero. Friction is only needed to change the rotational motion, as when the sphere rolls down an incline.

Another doubt I got is the following: I understand that it is the torque due to friction that helps a body roll. Hence, friction actualy helps motion.. Then why does the rolling body ever come to stop??

The static friction helps to prevent slipping, which also converts some mechanical energy into rotational kinetic energy. It doesn't help it go faster, if that's what you are thinking. (I'm talking about just rolling a ball along a surface, assuming no internal power source.) In real life, static friction is not the only force acting on the ball--the surfaces deform and produce what is called rolling friction, which does act as a dissipative force. (And of course there is also air resistance.)

 

[ZapperZ]

Hi,

I got a doubt while studying rotational mechanics. It is said in my book that when a sphere is purely rolling on a surface, total mechanical energy is conserved even though friction is acting. Isnt friction an external force? How can energy be conserved then??

The frictional force is there simply to prevent slipping. It does NO WORK onto the system. If it slips, then yes, the frictional force affects the energy content of the system. But if it rolls without slipping, the frictional force does no work.

Zz.

 

[haiha]

The friction here is static one, so it does not involve any relative movement that's why the energy is preserved. Sliding friction then will consume energy.

 

[regor60]

Yes, friction is an external force. But as long as there is no slipping, the static friction does no work and thus does not affect the mechanical energy.

Note that when the sphere is rolling along a horizontal surface, the static friction is zero. Friction is only needed to change the rotational motion, as when the sphere rolls down an incline.


The static friction helps to prevent slipping, which also converts some mechanical energy into rotational kinetic energy. It doesn't help it go faster, if that's what you are thinking. (I'm talking about just rolling a ball along a surface, assuming no internal power source.) In real life, static friction is not the only force acting on the ball--the surfaces deform and produce what is called rolling friction, which does act as a dissipative force. (And of course there is also air resistance.)

Are you sure the static friction is zero for a rolling sphere on a horizontal surface ? Doesn't the static friction depend only on normal force and coefficient ? If the force is zero, won't the ball stop rolling but the center of mass continue, eg. ball on ice ?

 

[Hootenanny]

Are you sure the static friction is zero for a rolling sphere on a horizontal surface ? Doesn't the static friction depend only on normal force and coefficient ? If the force is zero, won't the ball stop rolling but the center of mass continue, eg. ball on ice ?

Doc Al didn't say that the static frictional force was zero, he said that the static frictional force does no work on the system

 

[Doc Al]

Are you sure the static friction is zero for a rolling sphere on a horizontal surface ?

Yep. Once the sphere is rolling without slipping it will continue without the need for any applied force. (If the static friction were not zero, the sphere would accelerate.)

Doesn't the static friction depend only on normal force and coefficient ?

The maximum static friction force is given by \mu N, but the actual value of static friction can be anything from zero up to that maximum.

If the force is zero, won't the ball stop rolling but the center of mass continue, eg. ball on ice ?

No. Just like translational motion doesn't require a force to maintain constant speed, rotational motion does not require a torque to maintain constant angular speed. (This is Newton's 1st law at work.)

In fact, as I mentioned above, if the force were nonzero the ball would have to accelerate.

Doc Al didn't say that the static frictional force was zero, he said that the static frictional force does no work on the system

Actually, I did say that the static frictional force was zero--and I meant it.

 

[Hootenanny]

Actually, I did say that the static frictional force was zero--and I meant it.

Ahh yes, my bad. I should really read the whole post before throwing my comments in

 

[regor60]

Yep. Once the sphere is rolling without slipping it will continue without the need for any applied force. (If the static friction were not zero, the sphere would accelerate.)

So I'll persist. By saying "rolling without slipping" aren't you assuming a force to prevent it from slipping ? What if the ball rolls off a table - the ball continues to move forward and still spins, but you wouldn't say it's "rolling" - Isn't the air like a surface but with no friction from just the horizontal point of view ?

Also, a ball at rest on a table experiences a static friction force, doesn't it ? But it doesn't accelerate, does it, unless acted on by another force ? This seems at odds with your paren comment

 

[Doc Al]

So I'll persist. By saying "rolling without slipping" aren't you assuming a force to prevent it from slipping ?

Only when needed. Once it's rolling at the correct rate--to match it's translational speed--a friction force is no longer needed.

On the other hand, if the ball were were rolling down an incline then it would slip if there were no friction since it speeds up as it rolls down. A friction force is needed to make it spin faster to match it's translation to prevent slipping. (Of course, the friction also slows down the translation.)

Also, a ball at rest on a table experiences a static friction force, doesn't it ? But it doesn't accelerate, does it, unless acted on by another force ? This seems at odds with your paren comment

No, a ball at rest does not experience static friction. And if it did, it would have to accelerate!

Consider this: Put a block on a table. What static friction acts on it? None! Now if you start to push the block, that's when static friction begins to act to prevent slipping. The harder you push, the greater the static friction. Up until the maximum static friction the surfaces can provide, which is given by \mu N.