# Acceleration of Cylinder Rolling Horizontally: Analyzing Forces

• Tonyt88
In summary, the conversation discusses the horizontal acceleration of a cylinder with radius R rolling on a surface with kinetic friction of u(mu). The horizontal acceleration is found to be u*g, and it is also equal to r (alpha_z). However, the book gives a solution of -2 u*g/R for alpha_z. The reasoning behind this solution is not clear. The conversation also mentions a related problem where the cylinder is initially slipping completely, and the distance it rolls before slipping stops needs to be calculated. The request is made to use the homework posting template.
Tonyt88
You have a cylinder (with radius R) rolling horizontally on a surface with kinetic friction of u(mu). I understand that the horizontal acceleration is u*g b/c:

ma = u*(mg)
a = u*g

and then you have

a = r (alpha_z)

thus I'd figure alpha_z is just u*g/R, but the book gives a solution of:

-2 u*g/R

Basically, what's the reasoning?

Also, I have this problem related to this previous problem:

The cylinder is initially slipping completely, so initially omega_z = omega_o but v_x = 0. Rolling without slipping sets in when v_x = R(omega_z). Calculate the distance the cylinder rolls before slipping stops.

Cool.

Oh yeah, could you please use the homework posting template? Thanks.

## 1. What is the formula for calculating acceleration of a cylinder rolling horizontally?

The formula for calculating acceleration of a cylinder rolling horizontally is a = (F - μkmg)/m, where F is the applied force, μk is the coefficient of kinetic friction, m is the mass of the cylinder, and g is the acceleration due to gravity.

## 2. How does the coefficient of kinetic friction affect the acceleration of a rolling cylinder?

The coefficient of kinetic friction, μk, is a measure of the resistance to motion between two surfaces in contact. As the coefficient of kinetic friction increases, the force required to overcome this resistance also increases, resulting in a decrease in the acceleration of the rolling cylinder.

## 3. What other forces should be considered when analyzing the acceleration of a rolling cylinder?

In addition to the applied force and the coefficient of kinetic friction, other forces such as air resistance, rolling resistance, and any external forces acting on the cylinder should be taken into consideration when analyzing its acceleration.

## 4. How does the mass of the cylinder affect its acceleration?

The mass of the cylinder directly affects its acceleration, as seen in the formula a = (F - μkmg)/m. A larger mass will require a larger force to achieve the same acceleration as a smaller mass.

## 5. Can the acceleration of a rolling cylinder be negative?

Yes, the acceleration of a rolling cylinder can be negative if the applied force is less than the force of friction acting against it. This would result in the cylinder slowing down or decelerating instead of accelerating.

Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
13
Views
1K
• Mechanics
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
39
Views
2K
• Mechanics
Replies
4
Views
1K
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
207
• Mechanics
Replies
37
Views
2K
• Introductory Physics Homework Help
Replies
97
Views
3K