# -friction Is Independant Of Surface Area-

## Main Question or Discussion Point

----friction Is Independant Of Surface Area------

>> can anyone tel y friction is independant of surface area/length ......

thx an regards,

arun

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thank u sir ...to rephrase my question to get a still better explnation (wit regard to myself) .....

>> why is rolling better than sliding ??

thx and regards,

arun

arildno
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Rolling is better than sliding, because in rolling, friction merely CONVERTS translational kinetic energy into rotational energy without net energy loss, wheres in sliding, the object loses kinetic energy.

thank u sir,
my question is why does while sliding ,kinetic energy is lost as (friction) heat energy....why not while rollin????

thanks and regards,

arun

arildno
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Let S be a system of N particles, and let $\vec{F}_{i}$ be the net force acting upon the i'th particle.
The system's S rate of change of kinetic energy equals the sum of the particles' rates of change of kinetic energy.
Thus, if $K_{i}$ is the kinetic energy of the i'th particle, the rate of change is:
$$\frac{dK_{i}}{dt}=\frac{d}{dt}(\frac{m_{i}\vec{v}_{i}^{2}}{2})=m_{i}\vec{a}_{i}\cdot\vec{v}_{i}=\vec{F}_{i}\cdot\vec{v}_{i}$$
where $\vec{v}_{i},\vec{a}_{i},m_{i}$ is the i'th particle's velocity, acceleration and mass, respectively.

Now, the frictional force acting upon an object (or system S) acts upon the the "particle" directly in contact with the ground. Since the particle at the contact point is MOMENTARILY AT REST, its velocity is 0, and hence, the frictional force acting upon it cannot change its OR THE REST OF THE SYSTEM's kinetic energy! Otherwise stated, in rolling, friction does NO WORK.

In sliding, however, the particle at the contact point has a non-zero velocity, and hence, the friction force does non-zero work on the particle, and hence on the system as well.