# Homework Help: Why does an object move faster translational vs. rotational

1. Dec 11, 2015

### PhysicsInNJ

1. The problem statement, all variables and given/known data
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

2. Relevant equations
KE= 1/2mv^2
KEr= 1/2 Iw^2

3. The attempt at a solution
n/a

2. Dec 11, 2015

### 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.

3. Dec 11, 2015

### 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.

4. Dec 11, 2015

### 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?

5. Dec 11, 2015

### ehild

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,

6. Dec 11, 2015

### 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!

7. Dec 12, 2015

### haruspex

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.

8. Dec 12, 2015

### 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.

9. Dec 12, 2015

### haruspex

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