Rolling, Torque, and Angular Momentum (Physics Question)

[vladittude0583]

Hey guys, I am having a little hard time understanding a concept dealing with translational and rotational motion. For instance, if we have a solid sphere rigid body rolling down on an incline, we have both translation kinetic energy with regards to the center of mass and that of rotational kinetic energy associated with the particles of the sphere. Anyhow, my textbook mentions that it is static friction involved in ensuring this rigid body rolls "smoothly" down the incline without slipping. My question is, why is it static friction? I thought static friction needs to be overcome for a body to start moving? Can someone clarify this? Thanks.

[MATTYBLU2]

[MatrixS2000]

Think of it this way...static friction is what you rely on to take corners with your car. The tires rely on this to change the direction of the car. If it wasn't friction, you wouldn't be able to turn your car, you would turn the wheel, your tires would turn but you would just plow ahead. Keep in mind that this friction can be overcome. If you enter a corner to quickly, even though you may have turned the wheels, you have too much momentum and the car will plow forward. This is called understeer.

Another example...static friction is also used to stop your car. Your brakes clamp onto the rotor and does most of the work, but the friction between the road and your tires, keeps your tires turning. If it wasn't for that, the wheels would lock up instantly and you would have no control over your car - which is why ABS exists...but that is another story.

[vladittude0583]

Originally Posted by MatrixS2000

Think of it this way...static friction is what you rely on to take corners with your car. The tires rely on this to change the direction of the car. If it wasn't friction, you wouldn't be able to turn your car, you would turn the wheel, your tires would turn but you would just plow ahead. Keep in mind that this friction can be overcome. If you enter a corner to quickly, even though you may have turned the wheels, you have too much momentum and the car will plow forward. This is called understeer.

Another example...static friction is also used to stop your car. Your brakes clamp onto the rotor and does most of the work, but the friction between the road and your tires, keeps your tires turning. If it wasn't for that, the wheels would lock up instantly and you would have no control over your car - which is why ABS exists...but that is another story.

Well, after researching friction involved with rolling motion, I am under the assumption that if we have static friction involved in rolling motion which causes a rigid body to undergo pure rolling motion, then am I correct to postulate that this "static friction" helps keep the rigid body's center of mass under constant velocity because the maximum static friction force would be needed to have acceleration right?

[MatrixS2000]

Originally Posted by vladittude0583

Well, after researching friction involved with rolling motion, I am under the assumption that if we have static friction involved in rolling motion which causes a rigid body to undergo pure rolling motion, then am I correct to postulate that this "static friction" helps keep the rigid body's center of mass under constant velocity because the maximum static friction force would be needed to have acceleration right?

If I am reading your post correctly I would say no because you need to apply constant acceleration to keep it moving. If you didn't the friction would cause it to stop. Just like letting off the gas will cause your car to slow down and eventually stop.

[Aaron]

I think I know what class I'm not taking next year.

[Mr. Hanky]

The only thing that is implied when it comes to "static friction", is that 2 surfaces are NOT slipping. So if the rolling object has a diameter of d, then the angular velocity and translational velocity are simply governed by v=w*d/2 (v is velocity, w is omega or rotational velocity).

If the velocity is constant, then there will be a constant rotational velocity. If there is acceleration, then there will be a corresponding rotational acceleration. Under a no slip condition, the v=w*d/2 relation is in effect, at all times. When slip does occur, then this relation no longer holds true (and you then have to involve a dynamic friction coefficient and angular + translational acceleration/deceleration).

[Mr. Hanky]

Originally Posted by vladittude0583

My question is, why is it static friction? I thought static friction needs to be overcome for a body to start moving? Can someone clarify this? Thanks.

To address this comment directly, this is more in the context of 2 flat objects in contact with each other (though it is still technically true for a round + flat object). If 2 flat objects are in contact with static friction, then that friction must be overcome by a greater force to get them moving (sliding against each other).

In the case of the round + flat object, motion can occur while still under static friction, because the round object can freely rotate at whatever speed/acceleration it needs to, in order to keep that 1 point of contact with flat object in a technically static friction mode. (To be absolutely explicit, the velocity at the point of contact on the round object exactly matches the velocity of the flat object- hence, they are theoretically "stationary" with respect to each other).

Now if the round object cannot freely rotate, then the case becomes similar to the 2 flat objects scenario. Nothing is going to move until the static friction is overcome, which will result in the round object sliding (but not necessarily rolling) across the flat object.

[Brandon B]

Originally Posted by MatrixS2000

Another example...static friction is also used to stop your car. Your brakes clamp onto the rotor and does most of the work, but the friction between the road and your tires, keeps your tires turning. If it wasn't for that, the wheels would lock up instantly and you would have no control over your car - which is why ABS exists...but that is another story.

To clarify that a bit, once the lateral force applied to your tires' contact patch is enough to break them loose, the force between them and the road becomes kinetic friction which is generally much lower, although I wouldn't say you'd have NO control over your car, just a lot less. Drifting is a viable motorsport after all.

[vladittude0583]

Originally Posted by Mr. Hanky

The only thing that is implied when it comes to "static friction", is that 2 surfaces are NOT slipping. So if the rolling object has a diameter of d, then the angular velocity and translational velocity are simply governed by v=w*d/2 (v is velocity, w is omega or rotational velocity).

If the velocity is constant, then there will be a constant rotational velocity. If there is acceleration, then there will be a corresponding rotational acceleration. Under a no slip condition, the v=w*d/2 relation is in effect, at all times. When slip does occur, then this relation no longer holds true (and you then have to involve a dynamic friction coefficient and angular + translational acceleration/deceleration).

So, when you say "under a no slip condition," given by your explanation, then we should have constant angular velocity right? Only when slipping does occur should we have acceleration?

[vladittude0583]

Originally Posted by Mr. Hanky

To address this comment directly, this is more in the context of 2 flat objects in contact with each other (though it is still technically true for a round + flat object). If 2 flat objects are in contact with static friction, then that friction must be overcome by a greater force to get them moving (sliding against each other).

In the case of the round + flat object, motion can occur while still under static friction, because the round object can freely rotate at whatever speed/acceleration it needs to, in order to keep that 1 point of contact with flat object in a technically static friction mode. (To be absolutely explicit, the velocity at the point of contact on the round object exactly matches the velocity of the flat object- hence, they are theoretically "stationary" with respect to each other).

Now if the round object cannot freely rotate, then the case becomes similar to the 2 flat objects scenario. Nothing is going to move until the static friction is overcome, which will result in the round object sliding (but not necessarily rolling) across the flat object.

Let me make sure I am understanding this clear. Regarding your last paragraph, what you are saying is that if the round object is not free to rotate about some given axis, assuming static friction has been overcome at this point, then we are basically back to translational motion right where we can visualize the motion of the object as if all the mass was at the center of mass right?

Regarding your second paragraph, what did you mean exactly when you said the velocity at the bottom of the rigid object matches the velocity of the contact ground? From what I can recall, I thought it was the fact that the tangential velocity at the bottom of the object is the direct opposite of the translational velocity at the bottom of the object. Therefore, adding these two vector velocities results in zero velocity for the bottom point of the rigid object where it is in contact with the ground?

[iNCREDiPiNOY]

I loved Physics!

[Grubert]

Originally Posted by vladittude0583

Anyhow, my textbook mentions that it is static friction involved in ensuring this rigid body rolls "smoothly" down the incline without slipping. My question is, why is it static friction? I thought static friction needs to be overcome for a body to start moving? Can someone clarify this? Thanks.

Because at the contact point there is no movement. In other words, the speed of the point of the ball making contact with the incline is always zero. Otherwise it would be sliding + spinning, which it's not.

Therefore no relative movement -> static friction applies.

Simple as that.

[MatrixS2000]

Originally Posted by Brandon B

Drifting is a viable motorsport after all.

Not to a real track junkie!

BTW, since only the back end is sliding around all the time in drifting they are 100% relying on the front wheels to steer the car (while when real tracking , you use the front end and the back end to steer the car). That is why you see opposite lock most of the time from drifters, while with real tracking you use opposite lock to correct the back end when it slips out.

If the front end was also drifting, which it would be without any static friction, you would have no control over the car....an example of this is a car sliding on ice.

[Shadowself]

Originally Posted by vladittude0583

Hey guys, I am having a little hard time understanding a concept dealing with translational and rotational motion. For instance, if we have a solid sphere rigid body rolling down on an incline, we have both translation kinetic energy with regards to the center of mass and that of rotational kinetic energy associated with the particles of the sphere. Anyhow, my textbook mentions that it is static friction involved in ensuring this rigid body rolls "smoothly" down the incline without slipping. My question is, why is it static friction? I thought static friction needs to be overcome for a body to start moving? Can someone clarify this? Thanks.

You're making this more difficult than it needs to be.

While this can be explained in many complex ways, the answer is actually quite simple: The instantaneous point of contact of the rolling body does not move with respect to the instantaneous point of contact of the surface upon which it is rolling -- thus static friction.

IF the object (whatever that object is) is rolling without slipping, then a fraction of a second later a *different* instantaneous point of contact on the rolling body does not move with respect to the *different* instantaneous point of contact of the surface upon which it is rolling. The points of contact on each surface (on the rolling object and on the surface) change with time. However at any single instant the points of contact on each object do not move with regard to each other.

Static friction is 100% independent of any acceleration. (You can have static friction for either a ball rolling across a level table at constant velocity, and you can have static friction for a ball rolling, and accelerating, down a steeply inclined ramp.)

Static friction is 100% independent of angular momentum. (You can have static friction for a solid cylinder rolling down an inclined ramp, and you can have static friction for a hollow tube of the same mass and moment of inertia rolling down the same inclined ramp.)

Static friction is even 100% independent of transfer of energy. (You can have static friction for a solid cylinder rolling down an inclined ramp, and you can have static friction for a cylinder filled with a viscous fluid rolling down that same ramp.

This is a fun experiment to show first year engineering and physics majors: take two cans of food both with the same size and shape can and with the same mass; however, choose the two cans to have very different viscosities inside (say chili or beans [something relatively solid, but not 100% solid] and tomato soup [something relatively liquid]); on a rather wide and long inclined plane start both side by side at the top of the plane letting them both start rolling at the same moment; make sure the plane is not inclined so much that you break static friction; which one gets to the half way point first?; what's the cause of this?; which one gets to the bottom first? (assuming a relatively *long* plank); what's the cause of this? Now take it one step further: allow the two cans to roll unimpeded on a level plane for a significant distance after they reach the bottom of the inclined plane. Which one traverses some significant distance (say 5 meters or more) first? What's the cause of this?

And remember -- all this involves static friction!

[Mr. Hanky]

Originally Posted by vladittude0583

So, when you say "under a no slip condition," given by your explanation, then we should have constant angular velocity right? Only when slipping does occur should we have acceleration?

This is explained well by others above, but the gist is that there is NO restriction to constant angular velocity or acceleration while in a no slip condition. If there is constant angular velocity in the rolling object, that simply translates to constant translational velocity. If there is angular acceleration in the rolling object, that simply translates to translational acceleration.

The static friction only applies to the single point of contact between the circle and flat object (not to the entire system, which is certainly in motion...I think this distinction is where the confusion stems from). The velocity at this one point is completely matched (you can either say the relative velocity is zero, or the absolute velocities are equal), by the inherent behavior of "rolling".

They are equal AND moving in the same direction. They cannot be going the opposite direction (as per your inquiry in your following post), otherwise the 2 objects would most certainly be sliding (in which case, this is an entirely different scenario from the on in your original post).

The forces at this point of contact could be equal and opposite, though. Perhaps, that is what you had in mind?

[Mr. Hanky]

Originally Posted by vladittude0583

Let me make sure I am understanding this clear. Regarding your last paragraph, what you are saying is that if the round object is not free to rotate about some given axis, assuming static friction has been overcome at this point, then we are basically back to translational motion right where we can visualize the motion of the object as if all the mass was at the center of mass right?

This is pretty much right. Also bear in mind the possibility, that the round object can also be rotating AND sliding, if it is allowed to rotate, but not rotate freely. The round object could have constant angular velocity or angular acceleration, as well. If the latter, then the moment inertia of the rotational mass will be in play, as well as the inertia of the translational motion.

That scenario may be getting beyond the scope of what you are currently studying, though. That would be the "dynamic motion" case, whereas you may be focusing in on the "static motion" case, for now (constant velocities/forces in balance). So don't spend too much time figuring out what that dynamic motion case means, if it is outside your scope (that time will come in due time ).

[Brandon B]

Originally Posted by MatrixS2000

If the front end was also drifting, which it would be without any static friction, you would have no control over the car....an example of this is a car sliding on ice.

Nope, no static friction does not equal no friction. You still have a small amount of control, even under full kinetic friction conditions (all 4 wheels locked up and broken loose on a wet road for instance).

On ice, you would be close enough to zero control to call it zero, but under other sliding conditions, you still have a bit of control. A good example would be doing a burnout from standing start. You car will still accelerate (you control this with the gas pedal), even if it is at a greatly reduced amount until the tires catch.

BB

[Ratdaddy]

Please study the dynamics of bowling....It will answer all of your questions....
The equation to find the kinetic friction is : µk=Fk/mg. µk stands for the coefficient of kinetic friction and Fk stands for the Force due to kinetic friction,m is the mass of the ball and g stands for gravity.

[MatrixS2000]

Originally Posted by Brandon B

Nope, no static friction does not equal no friction. You still have a small amount of control, even under full kinetic friction conditions (all 4 wheels locked up and broken loose on a wet road for instance).

On ice, you would be close enough to zero control to call it zero, but under other sliding conditions, you still have a bit of control. A good example would be doing a burnout from standing start. You car will still accelerate (you control this with the gas pedal), even if it is at a greatly reduced amount until the tires catch.

BB

True, I should not have said no friction but a little friction...or the car would never slow down, which is again impossible while on the planet....