Rolling Motion: Difference between revisions
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==The Main Idea== | ==The Main Idea== | ||
Rolling motion is the turning motion of a round object such as a sphere or cylinder along a surface against which it is pressed. The rotation of a rolling object is the result of [[Friction]] between its edge and the surface, which applies a [[Torque]]. When rolling happens without slipping, this friction is [[Static Friction]] because the edge of the rolling object does not move relative to the surface. The point of contact between the object and the surface constantly changes but does not slide. Sometimes, slipping does occur. This can happen if, for example, the object was already moving with an arbitrary [[Angular Velocity]] when it came into contact with the surface, or if the object is accelerated along the surface so quickly that the maximum static friction force cannot cause a sufficient corresponding | Rolling motion is the turning motion of a round object such as a sphere or cylinder along a surface against which it is pressed. The rotation of a rolling object is the result of [[Friction]] between its edge and the surface, which applies a [[Torque]]. When rolling happens without slipping, this friction is [[Static Friction]] because the edge of the rolling object does not move relative to the surface. The point of contact between the object and the surface constantly changes but does not slide. Sometimes, slipping does occur. This can happen if, for example, the object was already moving with an arbitrary [[Angular Velocity]] when it came into contact with the surface, or if the object is accelerated along the surface so quickly that the maximum static friction force cannot cause a sufficient corresponding angular acceleration. In these situations, a [[Kinetic Friction]] force acts between the edge of the object and the surface. This kinetic friction force attempts to reduce the relative motion between the object's edge and the surface by adjusting the angular velocity of the object. Eventually, if no other forces act on the object or the surface, the angular velocity will be such that the object no longer slips. | ||
===A Mathematical Model=== | ===A Mathematical Model=== | ||
Revision as of 13:38, 9 July 2019
This page describes the motion of rolling objects, including the forces acting on them and the types of energy they have.
The Main Idea
Rolling motion is the turning motion of a round object such as a sphere or cylinder along a surface against which it is pressed. The rotation of a rolling object is the result of Friction between its edge and the surface, which applies a Torque. When rolling happens without slipping, this friction is Static Friction because the edge of the rolling object does not move relative to the surface. The point of contact between the object and the surface constantly changes but does not slide. Sometimes, slipping does occur. This can happen if, for example, the object was already moving with an arbitrary Angular Velocity when it came into contact with the surface, or if the object is accelerated along the surface so quickly that the maximum static friction force cannot cause a sufficient corresponding angular acceleration. In these situations, a Kinetic Friction force acts between the edge of the object and the surface. This kinetic friction force attempts to reduce the relative motion between the object's edge and the surface by adjusting the angular velocity of the object. Eventually, if no other forces act on the object or the surface, the angular velocity will be such that the object no longer slips.
A Mathematical Model
What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.
A Computational Model
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Examples
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