# Rolling a cylinder down a incline

1. Nov 20, 2009

### MatthewQueen

if a cylinder rolls down and incline without slipping

then i decrease the coefficient of friction and it does slip a little will it have more, less, or the same kinetic energy as before

I think less, my physics teacher says the same

2. Nov 20, 2009

### xxChrisxx

Welcome.

What is the formula for kinetic energy? Why do you think it will have less?

3. Nov 20, 2009

### IPhO' 2008

If a cylinder doesn't slip its kinetic energy won't decrease.
If a cylinder slip its kinetic energy will decrease.

4. Nov 20, 2009

### MatthewQueen

if you dont know the formula for kinetic energy then you cannot help me

5. Nov 20, 2009

### MatthewQueen

that's what i thought, can you explain why?
my physics teacher wont believe me

6. Nov 20, 2009

### xxChrisxx

I know what the formula is.

So explain your reasoning as to why you think that the kinetic energy will decrease.

7. Nov 20, 2009

### MatthewQueen

.5mv^2 and .5Iw^2

8. Nov 20, 2009

### MatthewQueen

because its slipping and there is friction

9. Nov 20, 2009

### MatthewQueen

we arent considering air resistance

10. Nov 20, 2009

### Bob S

Above a certain slope angle, the cylinder will stop rolling and slide. Find the angle.
Bob S

11. Nov 20, 2009

### rcgldr

If the friction is non-zero and there is slippage, then some of the energy is converted into heat by the sliding friction. You mention the two components of kinetic energy, linear and angular. You should work out an example, for a given angle and coefficient of dynamic friction (assume the initial state involves sliding), what is the energy lost due to friction (mgh - total energy of cylinder when it reaches bottom of incline)?

Last edited: Nov 20, 2009
12. Nov 20, 2009

### Phrak

Hmm. MatthewQueen is asking for a formula.

First;
If there is no friction, there is no energy lost to heat.
If there is 100% rolling friction, as in a lossless gear rolling down a rack, there is no energy lost to friction.

Secondly, the kinetic energy is less with any degree of rolling friction--100% or otherwise, as the potential energy is partitioned between the kinetic energy of the center of mass, and the rotational energy.

13. Nov 21, 2009

### IPhO' 2008

When the cylinder slipping , it similar to a box move on the ground. So when the cylinder slip. Some kinetic energy will lost to heat. The kinetic energy that lost to heat is fs
where f is the friction
s is the distance

14. Nov 21, 2009

### rcgldr

For a sliding box this is true, but for the cylinder that friction force is used to increase the angular kinetic energy, so the heat loss would be less than fs.

15. Nov 21, 2009

### IPhO' 2008

I think the increasing angular kinetic energy caused by the decreasing potential energy of the cylinder.
or have I misunderstood?

16. Nov 22, 2009

### rcgldr

Both linear and angular kinetic energy increase as gravitational potential energy decreases (as the cylinder rolls and slips down the incline). The question is how much energy is lost due to friction as heat for a given coefficient of dynamic friction and slope angle? Then again, if the answer is to simply know that the total energy of the cylinder will less in the case when friction converts some of the potential energy into heat, then knowing the exact amount of the loss isn't needed to answer the original question.

Last edited: Nov 22, 2009