Rigid body rotation about a moving axis

[Stevo6754]

Note this is physics I

This should be the right section as this is not homework..

Ok I'm having trouble understanding the concepts of rolling without friction, kinetic energy linear and kinetic energy rotational. I have a hard time following my professor in class and usually like to go over the notes we took but I've come to a example he did that I cannot understand. I uploaded pictures of my notes to make is easier on me and you.

As you can see its pretty much a sphere rolling up a friction incline plane, had to find the distance it rolled up the plane. That was no problem, calculations for that are on the right side of the page. Did U initial = zero and K final = 0; solved with no problem.

Now on the bottom left part of the page he asks what if the inclined plane was frictionless?
I don't understand where he got that KE rotation for KE final was not zero. He also states that if there is no kinetic friction force, each point of contact does not slide.

In the example where he takes away the friction on the incline. For his total change of KE he now leaves k final but only the k rotational part and not the k linear part. Why is this, I am very confused. Also if there is no friction wouldn't the object be sliding?

Thanks in advance

 

[renaissance]

First part.
I think the professor assumes that the inclined plane has no friction, so the rotational motion will never be changed. Initial condition determines the rotational KE, so final KE rotation is not zero.

The second part.
It can be seen the linear KE is related with the motion of the center of mass. The linear KE is changed due to the gravitational force which transform it into potential energy.

Hope my answer is conceivable. My first time here to answer questions and I am happy about it. :)

 

[dgOnPhys]

Note this is physics I

This should be the right section as this is not homework..

Ok I'm having trouble understanding the concepts of rolling without friction, kinetic energy linear and kinetic energy rotational. I have a hard time following my professor in class and usually like to go over the notes we took but I've come to a example he did that I cannot understand. I uploaded pictures of my notes to make is easier on me and you.

As you can see its pretty much a sphere rolling up a friction incline plane, had to find the distance it rolled up the plane. That was no problem, calculations for that are on the right side of the page. Did U initial = zero and K final = 0; solved with no problem.

Now on the bottom left part of the page he asks what if the inclined plane was frictionless?
I don't understand where he got that KE rotation for KE final was not zero. He also states that if there is no kinetic friction force, each point of contact does not slide.

One of the confusing things about rolling motion is that the point of contact is instantaneously at rest. So when the sphere is rolling w/o sliding (and changing velocity) the frictional force acting on the sphere is static friction. Only if the point of contact slides then the (smaller) kinetic (or dynamic) friction replaces static friction.
In absence of friction there is no way of changing the angular momentum of the sphere so it keeps rolling as it goes up the incline. The only force slowing down the sphere is the component of gravity parallel to the incline, it exerts no torque so it can only slow down the velocity of the center of mass but not rotation around it.

In the example where he takes away the friction on the incline. For his total change of KE he now leaves k final but only the k rotational part and not the k linear part. Why is this, I am very confused. Also if there is no friction wouldn't the object be sliding?

Thanks in advance

Yes the object will slide, meaning that the point of contact will not be at rest.

Please ask more if this or more is unclear

 

[Stevo6754]

One of the confusing things about rolling motion is that the point of contact is instantaneously at rest. So when the sphere is rolling w/o sliding (and changing velocity) the frictional force acting on the sphere is static friction. Only if the point of contact slides then the (smaller) kinetic (or dynamic) friction replaces static friction.
In absence of friction there is no way of changing the angular momentum of the sphere so it keeps rolling as it goes up the incline. The only force slowing down the sphere is the component of gravity parallel to the incline, it exerts no torque so it can only slow down the velocity of the center of mass but not rotation around it.

Yes the object will slide, meaning that the point of contact will not be at rest.

Please ask more if this or more is unclear

ah ok so that's where the KE rotation came from, thank you both for clearing this up.

 

[PJC01]

I can understand your confusion and I am happy to help clarify these concepts for you. Let's start with the basics: rigid body rotation about a moving axis. This refers to the motion of an object (in this case, a sphere) rotating around an axis that is also moving. This is different from a fixed axis rotation, where the axis of rotation remains stationary.

Now, let's move on to the concept of rolling without friction. When an object rolls without friction, there is no external force acting on it to slow it down or speed it up. This means that the object will maintain a constant velocity and will not slide or spin faster. The only forces acting on the object are the normal force (perpendicular to the surface it is rolling on) and the gravitational force (pulling it down).

Next, let's talk about kinetic energy (KE). In this example, the sphere has both linear and rotational kinetic energy. Linear KE refers to the energy of an object moving in a straight line, while rotational KE refers to the energy of an object rotating about an axis. In the first part of the example, the sphere is rolling with friction, so both the linear and rotational KE are present. However, in the second part where friction is removed, the sphere is still rolling but now there is no friction force, so the linear KE is zero. However, the sphere is still rotating, so the rotational KE is still present.

To address your question about the KE final not being zero, this is because the sphere is still rolling and thus has rotational KE, even though there is no linear KE. And since the sphere is not sliding without friction, there is no change in its linear velocity, so the final linear KE is also zero.

I hope this helps clarify the concepts for you. It's important to remember that in physics, it's common for one part of an equation to be zero while the other parts are still present. In this case, the absence of friction does not mean the absence of rotational motion. Keep practicing and asking questions, and you will continue to understand these concepts better. Good luck in your studies!