Rolling Motion of a Rigid Object

In summary, the conversation discusses the concept of rolling without slipping, which means that there is no sliding between the surfaces. The book mentions a relationship between rotational and translational motion in this scenario, but there is no simple relationship if there is slipping.
  • #1
Bashyboy
1,421
5
Hello,

I am currently reading about what was given in the title of this thread. In my book, it discusses the motion of a cylinder rolling on a surface without slipping; the cylinder is rotating about an axis, and it's center of mass has translational motion. What exactly do they mean rolling without slipping? The book also mentions a relationship between the rotational and translation motion when there is no slipping, what would happen if there was slipping? Why wouldn't there be a relationship if there was slipping?
 
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  • #2
Bashyboy said:
What exactly do they mean rolling without slipping?
Slipping means that the surfaces slide against each other; rolling without slipping means there's no sliding. The instantaneous speed of the point of contact with respect to the support surface is zero.
The book also mentions a relationship between the rotational and translation motion when there is no slipping, what would happen if there was slipping?
If the translational speed is just right compared to the rotational speed (v = ωr) then the surfaces will not slide or slip.
Why wouldn't there be a relationship if there was slipping?
There's no simple relationship if there is slipping.
 

1. What is the difference between rolling motion and sliding motion?

Rolling motion is the movement of a rigid object where it rotates and translates without slipping, while sliding motion is the movement of an object where it only translates without rotating.

2. What is the formula for calculating the velocity of a rolling object?

The formula for calculating the velocity of a rolling object is v = ωR, where v is the linear velocity, ω is the angular velocity, and R is the radius of the rolling object.

3. How does the shape of an object affect its rolling motion?

The shape of an object can affect its rolling motion by changing its moment of inertia. Objects with a larger moment of inertia require more torque to start rolling and have a slower rolling motion compared to objects with a smaller moment of inertia.

4. Can a rolling object accelerate?

Yes, a rolling object can accelerate. This is because when a rolling object experiences an external force, it can rotate and translate simultaneously, resulting in an increase in its velocity.

5. How does friction affect the rolling motion of an object?

Friction plays a crucial role in the rolling motion of an object. It provides the necessary torque for an object to start rolling and also acts against the rolling motion, slowing it down. The amount of friction depends on the surface and the normal force acting on the object.

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