Circular motion - velocity vector

[Poetria]

Homework Statement

Which of the following correctly describes the velocity vector in each case? 2. The attempt at a solution

I got it wrong at first.
My new attempt (I have a sneaking suspicion that I am missing something important):

For the first picture:

dtheta_1/dt<0 - the angle is decreasing
and
v=-r*dtheta_1/dt*theta_hat

for the second picture:
dtheta_2/dt>0 - the angle is increasing

v=-r*dtheta_2/dt*theta_hat - because the motion is clockwise

 

[Poetria]

For the first picture:

dtheta_1/dt<0 - the angle is decreasing
and
v=-r*dtheta_1/dt*theta_hat

Or I am wrong and it should be:

dttheta_1/dt<0 - slowing down
and
v=r*dtheta_1/dt*theta_hat because there are two minus sings: -dtheta_1/dt and minus sign - the negative direction of theta_hat

 

[haruspex]

I'm not at all sure what the question is.
Are the two figures exactly as given to you, or have you added some notation?
"Which of the following" implies some offered choices; what are they?
It also says "describes the velocity vector", but your suggested answers do not use any vector notation or terminology.

 

[Poetria]

I'm not at all sure what the question is.
Are the two figures exactly as given to you, or have you added some notation?
"Which of the following" implies some offered choices; what are they?
It also says "describes the velocity vector", but your suggested answers do not use any vector notation or terminology.

Yes, I should use Latex. :( I haven't added any notation.
There are four choices. The only difference is sings:

1.
v (vector) =r*dtheta_1/dt*theta-hat theta direction
v (vector) =-r*dtheta_2/dt*theta- hat

2.
v (vector) =r*dtheta_1/dt*theta-hat
v (vector) =r*dtheta_2/dt*theta-hat

3.
v (vector) =-r*dtheta_1/dt*theta-hat
v (vector) =-r*dtheta_2/dt*theta_hat

4.
v (vector) =-r*dtheta_1/dt*theta_hat
v (vector) =r*dtheta_2/dt*theta_hat

I have correctly deduced: dtheta_1/dt < 0 and dtheta_2/dt>0.
I am not sure if my reasoning is correct.

 

[haruspex]

deduced: dtheta_1/dt < 0 and dtheta_2/dt>0.

No, we do not know which way it is actually moving, nor even that it is moving. The task is to relate the variables so that they will agree on the movement.
The vector v is drawn such that its positive direction corresponds to a clockwise motion.
θ₁ is drawn such that an increase in its value corresponds to an anticlockwise motion. That in turn corresponds to a positive $\dot\theta_1$ in the $\hat\theta_1$ direction.
So what sign should connect $\dot\theta_1\hat\theta_1$ with $\vec v$?

 

[Poetria]

No, we do not know which way it is actually moving, nor even that it is moving. The task is to relate the variables so that they will agree on the movement.
The vector v is drawn such that its positive direction corresponds to a clockwise motion.
θ₁ is drawn such that an increase in its value corresponds to an anticlockwise motion. That in turn corresponds to a positive $\dot\theta_1$ in the $\hat\theta_1$ direction.
So what sign should connect $\dot\theta_1\hat\theta_1$ with $\vec v$?

The sign must be opposite to that of the vector v and therefore minus? I hope I got it.

 

[haruspex]

The sign must be opposite to that of the vector v and therefore minus? I hope I got it.

Yes.

 

[Poetria]

Great. Many thanks. I have one more but I have to think about it.