Wednesday, February 7, 2007

Breaking into motion - Part 1.

Breaking away in to motion.

This is a topic mainly about rotational dynamics.

Because as we know for a body to slide, the force reqd to start its motion is µ times the weight of the body, where µ is the co – efficient of static friction.

Now for a body to start rolling what should be the break away force that should be provided?.
Many believe that the force required should be enough to overcome static friction. I dont believe...
If that is the same as the a body to start sliding why our forefathers designed a wheel?

The explanation begins – ‘my explanation’

To make a body roll, some ‘external tendency should act’ – Torque, force – something… Here some cases are discussed.

The circular body is lying on the ground. A force (blue) is acting to move the body. Red arrow shows the reaction from the ground. The direction of reaction from the ground is arbitrary.

CASE 1.
Force acting at the lowest point of the body.


From experience we know, that we have to pull the lowest point with pretty high force and that it will start rolling in the clockwise direction, with skidding.


The lowest point in this case may get a velocity, so cannot be taken as the instantaneous centre of rotation.
A force acts from the ground in the opposite direction of F, the maximum value equal to the rolling friction force.
The body will tend to slip relative to ground, then the Static friction force acts at the points of slippage against the slip direction, which will counter the torque created by rolling friction force and the applied force.


But won’t that force add to the normal reaction, there by increasing the maximum static friction force available?

I must say that the additional force is parallel to the surface and will not add to normal reaction
.


Now about which point it will tend to rotate?
The point can be found out by constructing a triangle of force just before it starts rotating and finding out the point about which the torque is zero.

Now if the force F, is big enough to overcome the force of rolling and sliding friction, it will start accelerating towards left, but the body will rotate towards right because of the torque by the force F and Rolling friction.

After the force is released the body will start decelerating until the velocity at lowest point is zero and it start rolling towards right.

Now the Static friction force stop acting and the rolling friction will act towards left and reduce its velocity to zero.




CASE 1. A
Ground is rigid for the rolling body to deform.


In this case it will be pure sliding motion, because there is no torque to make it start rolling.

CASE 1. B
Both surface and body is rigid
.

Sliding in this case.

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