When a track goes round a level curve, the force of friction between the tyres and the road provides the necessary centripetal force. If the frictional force, which acts as centripetal force and keeps the body moving along the circular road is not enough to provide the necessary centripetal force, the car will skid. In order to avoid skidding while going round a curved path the outer edge of the road is raised above the level of the inner edge. This is known as banking of curved roads or tracks.
Let the surface of the road makes angle ፀ with horizontal surface. Then the normal force makes the same angle d with the vertical. When the car takes a turn, there are two forces acting on the car:
(a) Gravitational force mg (downwards)
(b) Normal force N (perpendicular to surface).
We can resolve the normal force into two components. N cos ፀ and N sin ፀ as shown in Figure. The component N cos ፀ balances the downward gravitational force 'mg' and component N sin ፀ will, provide the necessary centripetal acceleration. By using Newton second law
N cos ፀ = mg .....(1)
N sin ፀ = \(\frac { { mv }^{ 2 } }{ r } \)  ....(2)
Eq (2) / (1) ⇒ tan ፀ = \(\frac { { v }^{ 2 } }{ rg } \)
v= \(\sqrt { rg\tan\theta } \)
Need Banking of Tracks
1. The banking angle ፀ and radius of curvature of the road or track determines the safe speed of the car at the turning.
2. If the speed of car exceeds this safe speed, then it starts to skid outward but frictional force comes into effect and provides an additional centripetal force to prevent the outward skidding.
3. At the same time, if the speed of the car is little lesser than safe speed, it starts to skid inward and frictional force comes into effect, which reduces centripetal force to prevent inward skidding. 
4. However if the speed of the vehicle is sufficiently greater than the correct speed, then frictional force cannot stop the car from skidding.

Centripetal	Centrifugal forces
It is a real force which is exerted on the body by  the external agencies like gravitational force, tension in the string, normal force etc	It is a pseudo force or fictitious force which cannot arise from gravitational force, tension. force, normal force etc
Acts in both inertial and non-inertial frames	Acts only in rotating frames (non-inertial frame)
It acts towards the axis of rotation or center of the circle in Circular motion	It acts outwards from the axis of rotation or radially outwards from the center of the circular motion
\(\left| { F }_{ cp } \right| =m{ \omega }^{ 2 }r=\frac { { mv }^{ 2 } }{ r } \)	\(\left| { F }_{ cf } \right| =m{ \omega }^{ 2 }r=\frac { { mv }^{ 2 } }{ r } \)
Real force and has real effects	Pseudo force but has real effects
Origin of centripetal force is interaction between two objects	Origin of centrifugal force is inertia. It does not arise from interaction.
In inertial frames centripetal force has to be included when free body diagrams are drawn	In inertial frames there is no centrifugal force. In rotating frames, both centripetal and centrifugal force have to be included when free body diagrams are drawn.

Static friction: The opposing force that comes into play when one body tends to move over the surface of another, but the actual motion has yet not started is called static friction.
Limiting friction: If the applied force is increased the force of static friction also increases. If the applied force exceeds a certain (maximum) value, the body starts moving. This maximum value of static friction up to which body does not move is called limiting friction.
Kinetic or dynamic friction: If the applied force is increased further and sets the body in motion, the friction opposing the motion is called kinetic friction.
We can reduce friction
(1) By polishing.
(2) By lubrication.
(3) By proper selection of material.
(4) By streamlining the shape of the body.
(5) By using ball bearing.

\(F_{cp}=\frac{mv^2}{r}\)
\(F_{cp}=\frac{\frac{1}{4} \times(2)^2}{3}=0.333 \ N\)

v =\(\sqrt { (rg\quad tan\theta ) } =\sqrt { 20\times 9.8\times tan{ 15 }^{ 0 } } =\sqrt { 20\times 9.8\times 0.26 } \) = 7.1 ms^-1
The safe speed for the car on this road is 7.1 ms^-1

In a leveled circular road, skidding mainly depends on the coefficient of static friction \({ \mu }_{ s }\). The coefficient of static friction depends on the nature of the surface which has a maximum limiting value. If the speed of car exceeds this safe speed, then it starts to skid outward but frictional force comes into effect and provides an additional centripetal force to prevent the outward skidding. 
\(tan \ \theta> { \mu }_{ s }\)
When the tangent of the angle of banking is greater than the coefficient of friction, skidding occurs.

(a) A frame of reference which is at rest or which is moving with a uniform velocity along a straight line is called an inertial frame of reference.
(b) In the inertial frame of reference Newton's laws of motion holds good.
Example: The lift at rest, lift moving (up or down) with constant velocity, car moving with constant velocity on a straight road.

Limiting static/kinetic friction between any pair of dry unlubricated surfaces is independent of apparent area in contact.
Limiting static/kinetic friction between any pair of unlubricated surfaces depends on nature of material of the surfaces in contact.
Limiting static/kinetic friction between any pair of dry unlubricated surfaces is directly proportional to the normal reaction.
Static Friction: If Fs is static friction and R (N) is a normal reaction
Then
F_s ∝ R
∴ F_s = μ_sR
μ_s = coefficient of static friction.
∴ μ_s = \(\frac{F_s}{R}\)
The coefficient of static friction is defined as the ratio of the static friction to normal reaction
Kinetic friction: If Fs is static friction and R (N) is a normal reaction 
Then
F_k ∝ R
∴ F_k = μ_sR
μ_k = coefficient of static friction.
∴ μ_k = \(\frac{F_k}{R}\)
The coefficient of kinetic friction is defined as the ratio of the kinetic friction to normal reaction

Consider an inclined plane on which an object is placed as shown in the figure, Let the angle which this plane makes with the horizontal be ፀ. For small angle of ፀ, the object may not slide down. As ፀ is increased, for a particular value of ፀ, the object begins to slide down. This value is called angle of repose. Hence, the angle of repose is the angle of the inclined plane with the horizontal such that an object placed on it begins to slide.