# Rigid body rotation about a moving axis

• Stevo6754

#### 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?

#### Attachments

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. :)

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?

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