Rolling motion including torque and acceleration

• XxBollWeevilx
In summary, the problem involves a lawn roller being pushed with a constant horizontal force. The roller is a uniform solid cylinder with a radius R and mass M. The goal is to find the acceleration of the center of mass and the minimum coefficient of friction needed to prevent slipping. Taking the torque with respect to the center of mass can help with this problem. A force diagram may be helpful in understanding the rolling motion. It is unknown if the applied force creates any torque.
XxBollWeevilx

Homework Statement

A constant horizontal force $$\vec{F}$$ is applied to a lawn roller in the form of a uniform solid cylinder of radius R and mass M. If the roller rolls without slipping on the horizontal surface, show that (a) the acceleration of the center of mass is $$\frac{2\vec{F}}{3M}$$ and (b) the minimum coefficient of friction necessary to prevent slipping is $$\frac{F}{3Mg}$$. (Hint: Take the torque with respect to the center of mass.

Not quite sure.

The Attempt at a Solution

Well, this is my last problem of the night to finish. To be honest, i have no idea where to begin. I don't know how to examine the acceleration or how to use torque to find friction. Any step in a positive direction would be helpful. I appreciate it.

I was thinking maybe a force diagram...but I'm not sure how it would apply to the rolling motion.

Also, I'm not sure whether the applied force is causing any torque or not.

1. What is rolling motion?

Rolling motion is a type of motion in which an object moves along a surface while also rotating. This motion is seen in objects such as wheels, balls, and cylinders.

2. What is torque?

Torque is a measure of the force that causes an object to rotate around an axis or pivot point. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation.

3. How does torque affect rolling motion?

Torque is responsible for causing an object to start rolling and for maintaining its rotation. In order for an object to roll without slipping, the torque applied must be equal to the product of the object's moment of inertia and its angular acceleration.

4. What is the relationship between torque and acceleration in rolling motion?

In rolling motion, the torque applied to an object is directly proportional to its angular acceleration. This means that as the torque increases, the angular acceleration also increases, causing the object to roll faster.

5. How is rolling motion different from other types of motion?

Rolling motion is different from other types of motion because it involves both linear and rotational motion. This means that the object is moving along a surface while also rotating around its own axis. It also requires a torque to maintain its motion, whereas other types of motion may not.

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