Why does an object move faster translational vs. rotational

[PhysicsInNJ]

Homework Statement

In studying for an upcoming exam, one of the concepts introduced was that an object moving translationally will move faster than one moving rotationally. To me that doesn't make sense. So, I do not have a specific problem but really just looking for someone to be able to clarify this better

Homework Equations

KE= 1/2mv^2
KEr= 1/2 Iw^2

The Attempt at a Solution

n/a

 

[Mister T]

That makes no sense to me, either. Translational velocity and rotational velocity are measured in different units, so it doesn't make sense to say that one is bigger or smaller than the other.

 

[PhysicsInNJ]

A better way to phrase it, if two objects of equal mass, one a cylinder and one a block were placed atop an incline, the sliding block would reach the bottom before the rolling cylinder.

 

[Mister T]

That's not a different way to phrase it. That's a totally different statement and situation. Can you write expressions relating the kinetic energy of each object at the bottom of the incline to the potential energy at the top?

 

[ehild]

Homework Statement

In studying for an upcoming exam, one of the concepts introduced was that an object moving translationally will move faster than one moving rotationally. To me that doesn't make sense.

And it has no sense. What do you mean on "moving rotationally? "
You can speak of sliding, or rolling without slipping. And in case a sphere or cylinder slides down along a frictionless incline, or rolls down an incline of the same slope and height, et the end the center of mass of the sliding one will move faster than the CM of the rolling one. It is because conservation of energy. While the sliding body has only translational kinetic energy at the end, so 1/2 mv²=mgh, the rolling body has both translational + rotational KE, equal to mgh,

 

[PhysicsInNJ]

That's what I meant, the object rolling without slipping vs the object sliding. It makes sense and clears up my confusion that it has both translational + rotational energy. Thank you!

 

[haruspex]

A better way to phrase it, if two objects of equal mass, one a cylinder and one a block were placed atop an incline, the sliding block would reach the bottom before the rolling cylinder.

Still doesn't work for me.
If there is no friction then both objects will slide and reach the bottom at the same time.
If the static coefficient of friction is $<\frac{k^2\tan(\theta)}{r^2+k^2}$ both objects will still slide and reach the bottom at the same time. In this case the cylinder will be rotating.
If friction is sufficient to prevent the cylinder sliding, friction will slow the block more than it slows the cylinder.

 

[dean barry]

Another experiment in this area is :
A cylinder and a sphere are released side by side at the same time and roll without slipping down an incline, which reaches the bottom first ?
They have the same mass and radius.

 

[haruspex]

Another experiment in this area is :
A cylinder and a sphere are released side by side at the same time and roll without slipping down an incline, which reaches the bottom first ?
They have the same mass and radius.

Please don't introduce sidetracks, at least until the OP is settled. It just confuses the thread.