Circular motion of a Weightless rod

[PitViper]

Homework Statement

weightless rod AB of length a is free to rotate about a fixed end A. At its other end B, a particle of mass m is attached. B is connected to a ring C of mass m by an inelastic string of length a. The ring C slides smoothly along another fixed horizontal rod passing through A. Initially, points A, B, and C are aligned in a straight line with AC = 2a

The system is released from rest, and at time t, the angle CAB is θ.

Relevant Equations

(d/dt (theta)) ^ 2 = (2g)/a * (sin theta)/(1 + 4sin^2 theta)

I used law of conservation of energy to calculate (d theta/ dt)^2 (from:mgasin theta=1/2m(d theta/dt.a)^2+1/2mu^2(u is the velocity of the C ring at time=t)), but wasnt able to find u(velocity of C).Is there any relationship between the tangential velocity of B(d theta/dt.a) and velocity of C(u) that I'm missing?

 

[kuruman]

Please post a picture showing the physical system.

 

[PitViper]

Please post a picture showing the physical system.

 

[PitViper]

View attachment 347838

This is how I think It should look like.

 

[kuruman]

This is how I think It should look like.

Thank you for the drawing.

What are you asked to find? It is not clear from the statement of the problem.

Also, the drawing shows that the rod "after time = t" is horizontal. The statement of the problem says that the "weightless rod AB of length a is free to rotate about a fixed end A." Both cannot be correct. If the rod is free to rotate, it should be at some angle below the horizontal after some time has elapsed.

 

[TSny]

There are two rods. C slides on a fixed, horizontal rod of unspecified length. Particle B is at the end of a massless rod that is free to rotate in a vertical plane about A. Initially, this rod is horizontal so that the ring C is a distance 2a from A.

 

[kuruman]

There are two rods. C slides on a fixed, horizontal rod of unspecified length. Particle B is at the end of a massless rod that is free to rotate in a vertical plane about A. Initially, this rod is horizontal so that the ring C is a distance 2a from A.

Ah, I see it now. Thanks.

 

[TSny]

Is there any relationship between the tangential velocity of B(d theta/dt.a) and velocity of C(u) that I'm missing?

Let $x$ be the distance of C from A. Can you express $x$ in terms of $a$ and $\theta$?

 

[PitViper]

Let $x$ be the distance of C from A. Can you express $x$ in terms of $a$ and $\theta$?

2a cos theta?

 

[PitViper]

There are two rods. C slides on a fixed, horizontal rod of unspecified length. Particle B is at the end of a massless rod that is free to rotate in a vertical plane about A. Initially, this rod is horizontal so that the ring C is a distance 2a from A.

Yeah exactly!

 

[TSny]

2a cos theta?

Yes. Can you use this to get the relationship between the speeds of B and C?

 

[PitViper]

Yes. Can you use this to get the relationship between the speeds of B and C?

Hmmm I don’t quite get it

 

[TSny]

How do you get velocity from position?

 

[PitViper]

Hmmm I don’t quite get it

I can calculate the mean velocity of C by dividing displacement of C by t,but I don’t see how that can be ended up in final answer(the formula we have to prove)…

 

[PitViper]

How do you get velocity from position?

first derivative?

 

[PitViper]

first derivative?

Oh my god dude I got it

 

[PitViper]

Oh my god dude I got it

Thank you very much

 

[PitViper]

Thank you very much

This is it right?

 

[PitViper]

Can you please suggest me any problems to practice these type of questions?