# Is It Possible for a Cylinder to Roll Freely Without Slipping?

• Soaring Crane
In summary, the correct statement is: If a cylinder is rolling without slipping on a horizontal surface at a constant speed, the friction force must be zero. Therefore, choices b-d are false.
Soaring Crane
A cylinder is observed to be rolling freely at a constant speed on a horizontal surface. Which of the following statements is true?

a.It is possible that the cylinder is both rolling and sliding at the same time, i.e. that v, the speed of the centerpoint, is not = to rw.

b.If the cylinder is rolling without slipping, there must be a non-zero friction force exerted by the surface.

c.It is not possible for the cylinder to roll unless friction is present.

d.Even if the surface has friction, the cylinder cannot roll without slipping.

e.If friction is present it is not possible for the motion to occur without loss of energy.

Would the answer be b.? For rolling without slipping, static friction must be present.

Thanks.

Soaring Crane said:
For rolling without slipping, static friction must be present.
Careful. Note that the surface is horizontal.

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If a block is accelerated on a surface with friction and then hits a frictionless surface, it will continue with its velocity forever. A wheel on a horizontal surface only needs friction to accelerate

On a horizontal surface, can't rolling without slipping occur with and without friction?

Also, is it possible, as in choice A, for slipping and rolling to occur simultaneously like driving across an icy road?

Soaring Crane said:
On a horizontal surface, can't rolling without slipping occur with and without friction?
If you mean "Can rolling without slipping occur even when the surfaces are frictionless?", then yes, if the angular and translational speeds comply with $v = \omega r$.

But even if the surfaces are not frictionless, what friction force is needed to maintain rolling without slipping on a horizontal surface?

Also, is it possible, as in choice A, for slipping and rolling to occur simultaneously like driving across an icy road?
Yes, rolling and slipping can certainly occur together. Nowhere does it say that the cylinder necessarily rolls without slipping.

Since the cylinder rolls at a constant speed, what can you say about the friction force that acts on it?

Isn't there a rolling friction? Shoudn't it be kinetic friction if the horizontal surface is not frictionless?

Let me rephrase my question: Since the cylinder, we are told, is moving at a constant speed, what must be the net force on it? Given this, what must be the friction force on it?

If there is constant speed, the acceleration is 0, so the net force must be 0 N?

Right. And since the cylinder is rolling freely (meaning: nothing is pushing or pulling it), what must be the friction force?

The friction force would also be zero since it is the only other possible component in the horizontal direction? Does this mean that choices b-d are false?

Soaring Crane said:
The friction force would also be zero since it is the only other possible component in the horizontal direction?
Right.
Does this mean that choices b-d are false?
Yes.

## 1. What is rotational inertia and how does it relate to a cylinder's rotational motion?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to changes in rotational motion. In other words, it determines how difficult it is to change the rotational speed or direction of an object. For a cylinder, the rotational inertia depends on its mass, radius, and distribution of mass around its axis of rotation. The larger the rotational inertia, the more force is required to change the cylinder's rotational motion.

## 2. How does the shape of a cylinder affect its rotational motion?

The shape of a cylinder can significantly affect its rotational motion. The distribution of mass around the axis of rotation is a crucial factor in determining the cylinder's rotational inertia. A hollow cylinder has a larger rotational inertia than a solid cylinder with the same mass and radius. This is because more mass is located farther from the axis of rotation. Additionally, the shape of the cylinder can also affect its drag and stability, which can influence its rotational motion.

## 3. Can a cylinder have both linear and rotational motion?

Yes, a cylinder can have both linear and rotational motion at the same time. The linear motion occurs when the cylinder moves in a straight line, while rotational motion occurs when the cylinder rotates around its axis. These two types of motion can be combined, for example, when a cylinder rolls down a ramp. The cylinder's center of mass moves in a straight line, while the cylinder itself rotates as it moves.

## 4. How does the surface on which a cylinder rolls affect its rotational motion?

The surface on which a cylinder rolls can affect its rotational motion in several ways. If the surface is smooth, there will be less friction, allowing the cylinder to roll more easily. If the surface is rough, there will be more friction, making it harder for the cylinder to roll. Additionally, if the surface is inclined, the cylinder's weight will create a torque, causing the cylinder to accelerate or decelerate in its rotational motion.

## 5. Can a cylinder's rotational motion be affected by external forces?

Yes, a cylinder's rotational motion can be affected by external forces. Any force applied to the cylinder that is not aligned with its axis of rotation will create a torque, causing the cylinder to accelerate or decelerate in its rotational motion. The magnitude and direction of the external force will determine the effect on the cylinder's rotational motion. For example, a force applied tangentially to the cylinder's surface will cause it to spin faster, while a force applied in the opposite direction will cause it to slow down.

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