Determine the angular speed ##\dotθ## of the arm OC

[Alexanddros81]

Homework Statement

13.30 The colar B slides along a guide rod that has the shape of the spiral R = bθ.
A pin on the collar slides in the slotted arm OC. If the speed of the collar is constant at v₀,
determine the angular speed $\dot θ$ of the arm OC in terms of v₀, b, and θ.

Homework Equations

The Attempt at a Solution

The solution given: $(\frac {v_0} {b}) (1+θ^2)^{-1/2}$

What I have only done is : $v_R=\dot R=b \dotθ = v_0$
and $v_θ=R\dotθ$
Any hints?

 

[haruspex]

Homework Statement

13.30 The colar B slides along a guide rod that has the shape of the spiral R = bθ.
A pin on the collar slides in the slotted arm OC. If the speed of the collar is constant at v₀,
determine the angular speed $\dot θ$ of the arm OC in terms of v₀, b, and θ.

View attachment 211424

Homework Equations

The Attempt at a Solution

The solution given: $(\frac {v_0} {b}) (1+θ^2)^{-1/2}$

What I have only done is : $v_R=\dot R=b \dotθ = v_0$
and $v_θ=R\dotθ$
Any hints?

You are told the speed is v₀. $\dot R$ is only one component of that.

 

[Alexanddros81]

I guess this is correct.

 

[haruspex]

View attachment 211458

I guess this is correct.

Yes.