Confusion about circular motion

[sachin123]

Hello all,I am having a lot of confusion about circular motion.
Consider a hill which is perfectly circular at the top.
When a vehicle passes over it at constant velocity,at the top most point,
I want an expression for Normal reaction force by the hill on the vehicle.
I take a non inertial frame of reference.

mg-N-(mv^2)/r=0 is the equation(symbols have usual meanings).
I understand it(as (mv^2)/r is pseudo force acting upwards).
But,how do we write it wrt to an inertial frame of reference?

 

[Doc Al]

Why are you using a non-inertial frame?

Just stick to an inertial frame. What forces act on the vehicle? What is the vehicle's acceleration? Apply Newton's 2nd law.

 

[sachin123]

mg acts downwards and N upwards.They should together maintain a centripetal force:
(mv^2)/r
So,mg-N=(mv^2)/r ?
In this case we could identify the source of force,gravity.
But take this:
a coin on a table rotating about its axis.The coin slips away and falls down.How do you give equation to this?

 

[Doc Al]

mg acts downwards and N upwards.They should together maintain a centripetal force:
(mv^2)/r
So,mg-N=(mv^2)/r ?

Yes.

In this case we could identify the source of force,gravity.

OK.

But take this:
a coin on a table rotating about its axis.The coin slips away and falls down.How do you give equation to this?

You'll need to describe the problem in more detail. Is the table rotating? Just the coin?

 

[sachin123]

Yes,the table is rotating.A coin is placed over it.It falls off.
We know its radial acceleration is (mv^2)/r.But can you give an equation?
Problems for me is,there should be force to cause motion.Here absence of force is causing it.How do we write an equation then?

 

[Doc Al]

What force do you think exists between the table and the coin? If the coin were to remain on the rotating table, what force must be accelerating it?

 

[Doc Al]

More on this:

Yes,the table is rotating.A coin is placed over it.It falls off.
We know its radial acceleration is (mv^2)/r.But can you give an equation?

If the coin doesn't slide, it must be radially accelerated. Thus the net force on it will be given by Newton's 2nd law as mv^2/r. What force must act on the coin?

If the table rotates too fast, that force will be insufficient to keep the coin moving in a circle. The coin will start to slide off the table.

Problems for me is,there should be force to cause motion.Here absence of force is causing it.How do we write an equation then?

The coin is already moving. The lack of sufficient force prevents its motion from being kept in a circle--it just keeps going.

 

[NEILS BOHR]

its all abt NEWTON's laws...

 

[sachin123]

The force is friction.
So the coin need not necessarily accelerate outwards?It only moves with constant velocity right?
And,looking at it from an inertial view,the coin will it will come out tangentially right?

 

[sachin123]

I have this other problem where they ask the centrifugal force on a particle(m) rotating in a circle with radius a with ang speed x1 when seen from a frame rotating at ang speed x2.
Can you help me with this?I am clueless.

 

[Doc Al]

The force is friction.

Yes. As long as the static friction is sufficient to provide the needed centripetal force, the coin will stay in place with respect to the rotating table.

So the coin need not necessarily accelerate outwards?It only moves with constant velocity right?

If the coin moves in a circle, it must accelerate inward--centripetally. Its speed is constant, but its velocity is tangential and continually changing direction as it moves in its path.

And,looking at it from an inertial view,the coin will it will come out tangentially right?

If all of a sudden all friction were removed, then the coin would just continue moving tangentially, per Newton's 1st law. In real life, if the speed of rotation is increased, the coin will start to slide as its maximum static friction became inadequate to maintain its position. But it won't move in a straight line, since there would still be dynamic friction acting on it.

 

[Doc Al]

I have this other problem where they ask the centrifugal force on a particle(m) rotating in a circle with radius a with ang speed x1 when seen from a frame rotating at ang speed x2.
Can you help me with this?I am clueless.

Well, what's the formula for calculating centrifugal force?

 

[sachin123]

If the coin moves in a circle, it must accelerate inward--centripetally. Its speed is constant, but its velocity is tangential and continually changing direction as it moves in its path.

I was talking about it when it runs off the table.

If all of a sudden all friction were removed, then the coin would just continue moving tangentially, per Newton's 1st law. In real life, if the speed of rotation is increased, the coin will start to slide as its maximum static friction became inadequate to maintain its position. But it won't move in a straight line, since there would still be dynamic friction acting on it.

What if somehow we remove only the component of friction that is responsible for centripetal force(the radial part of friction).Then how would it move?

Dynamic friction would retard the motion.How would it change the path?