# Acceleration and Friction of a Rolling Cylinder

• hm8
In summary, the problem involves a lawn roller in the form of a thin-walled, hollow cylinder being pulled with a constant horizontal force by a handle attached to the axle. The goal is to find the acceleration and friction force when the roller rolls without slipping. The equations used are the moment of inertia for a hollow cylinder, the sum of torque, and the sum of forces. By substituting the acceleration as a fraction of the radius, the equation for friction force simplifies to F = Ma. However, when this is plugged back into the sum of forces equation, there seems to be a discrepancy.
hm8

## Homework Statement

A lawn roller in the form of a thin-walled, hollow cylinder with mass M is pulled horizontally with a constant horizontal force F applied by a handle attached to the axle.

a)If it rolls without slipping, find the acceleration.

b)If it rolls without slipping, find the friction force.

## Homework Equations

$I_{Hollow Cylinder} = MR^{2}$

$\sum \tau = f_{friction}R = I\alpha = MR^{2}\alpha$

$\sum F = F - f_{friction} = F = Ma$

## The Attempt at a Solution

I'm really not sure...it seems like I have too many unknowns (R, a, alpha, friction)

Ok, so I just remembered that because its not slipping, I can change $\alpha$ to $\frac{a}{r}$

so I get $f_{friction}R = MR^{2}*\frac{a}{R}$

which cancels down to $f_{friction} = Ma$

But when I plug that back into the other equation I just get F - ma = ma...

where did I go wrong?

Any help, guys?

## 1. What is the definition of acceleration?

Acceleration is the rate of change of velocity with respect to time. In other words, it is the measure of how quickly an object's speed or direction changes.

## 2. How does a rolling cylinder experience acceleration?

A rolling cylinder experiences acceleration due to the forces acting on it. As the cylinder rotates, its contact point with the ground moves forward, causing it to accelerate in the direction of its motion. In addition, any external forces acting on the cylinder, such as gravity or friction, can also contribute to its acceleration.

## 3. What is the relationship between acceleration and net force?

According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that the greater the net force acting on a rolling cylinder, the greater its acceleration will be.

## 4. How does friction affect the acceleration of a rolling cylinder?

Friction is a force that acts in the opposite direction of an object's motion. Since a rolling cylinder experiences friction between its surface and the ground, this force can slow down its acceleration. The amount of friction depends on the type of surface and the weight of the cylinder.

## 5. Can a rolling cylinder experience negative acceleration?

Yes, a rolling cylinder can experience negative acceleration, also known as deceleration or retardation. This occurs when the net force acting on the cylinder is in the opposite direction of its motion, causing it to slow down or come to a stop.

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