# Law of Motion XII

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Contact Force:- The forces acting between the two bodies due to the mutual contact of their surfaces are known as contact forces. The resultant of all the contact forces acting between the bodies is known as resultant contact force. Example friction (f) and normal reaction (N) are contact forces and their resultant (Fc) is the resultant is the resultant contact force
Since maximum value of frictional force is Limiting frictional force (µsN) Therefore maximum value of contact force is
Angle of Friction:- The angle between the resultant contact force (of normal reaction and friction) and the normal reaction is known as the angle of friction.
Angle of Repose:- The angle of the inclined plane at which a body placed on it just begins to slide is known as angle of repose.
Perpendicular to the plane
N = mgCosθ (since body is at rest)
Parallel to the plane when body is at rest
mgSinθ = fs
When body is just about to slide
Rolling Frictional Force:- Frictional force which opposes the rolling of bodies (like cylinder, sphere, ring etc.) over any surface is called rolling frictional force. Rolling frictional force acting between any rolling body and the surface is almost constant and is given by µrN. Where µr is coefficient of rolling friction and N is the normal reaction between the rolling body and the surface.
Note – Rolling frictional force is much smaller than maximum value of static and kinetic frictional force.
Cause of Rolling Friction:- When any body rolls over any surface it causes a little depression and a small hump is created just ahead of it. The hump offers resistance to the motion of the rolling body, this resistance is rolling frictional force. Due to this reason only, hard surfaces like cemented floor offers less resistance as compared to soft sandy floor because hump created on a hard floor is much smaller as compared to the soft floor.

Need to Convert Kinetic Friction into Rolling Friction:- Of all the frictional forces rolling frictional force is minimum. Hence in order to avoid the wear and tear of machinery it is required to convert kinetic frictional force into rolling frictional force and for this reason we make the use of ball-bearings.
Friction: A Necessary Evil:-
Although frictional force is a non-conservative force and causes lots of wastage of energy in the form of heat yet it is very useful to us in many ways. That is why it is considered as a necessary evil.

i) Friction is necessary in walking. Without friction it would have been impossible for us to walk.
ii) Friction is necessary for the movement of vehicles on the road. It is the static frictional force which makes the acceleration and retardation of vehicles possible on the road.
iii) Friction is helpful in tying knots in the ropes and strings.
iv) We are able to hold anything with our hands by the help of friction only.

i) Friction causes wear and tear in the machinery parts.
ii) Kinetic friction wastes energy in the form of heat, light and sound.
iii) A part of fuel energy is consumed in overcoming the friction operating within the various parts of machinery.

Methods to Reduce Friction:-
i) By polishing – Polishing makes the surface smooth by filling the space between the depressions and projections present in the surface of the bodies at microscopic level and there by reduces friction.
ii) By proper selection of material – Since friction depends upon the nature of material used hence it can be largely reduced by proper selection of materials.
iii) By lubricating – When oil or grease is placed between the two surfaces in contact, it prevents the surface from coming in actual contact with each other. This converts solid friction into liquid friction which is very small.

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