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## Homework Statement

A car goes on a horizontal circular road of radius ##R##, the speed increasing at a constant rate ##\frac{dv}{dt}=a##. The friction coefficient between the road and the tier is ##\mu##. Find the speed at which the car will skid.

## Homework Equations

## The Attempt at a Solution

I solved it earlier using the fact that only force acting on the system is the friction. So ##F_{net}=Ma_{net}##.

So ##f==m\sqrt { { a }^{ 2 }+\frac { { v }^{ 4 } }{ { R }^{ 2 } } } ##

And the car will slip when ##f=\mu mg##

Using these two equations I got the right answer.

But I am confused now.

According to my solution it seems that a component of friction force is providing the tangential acceleration. But friction always opposes the motion then how could it accelerate a body. I mean, it should always decelerate the body.

I have one more confusion.

It is well known that friction provides the required centripetal force to move a car in circle. But friction always always opposes the motion and in a small time the car moves in a tangential direction. So friction should act in tangential direction (opposite to the motion of the car). Why does it acts in radially inward direction.

In the above problem it is clear that a component of friction acts in tangential direction. But when a car moves in circle with a constant speed then friction acts in radial direction only. As the car moves in tangential direction in a small period of time so friction should act in tangential direction to oppose the motion of the car.

Please help!