The collar B slides along a guide rod (Polar Coord.)

[Alexanddros81]

Homework Statement

13.29 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 OC is rotating at the constant angular
speed $\dot θ = ω$, determine the magnitude of the acceleration of the collar when
it is a A.

Homework Equations

The Attempt at a Solution

[/B]

what a_θ will be?
It is not 2. I have just left it unfinished.

 

[kuruman]

$\dot{R}$ is not zero. Does $R$ not change as the collar slides?

 

[Alexanddros81]

$a_R = \ddot R - R\dot θ^2 = -\frac {π} {2} b ω^2$ since $R = bθ = bπ/2$ and $\dot R = b\dot θ = bω$ and $\ddot R = b\ddot θ = 0$

$a_θ = R\ddotθ + 2 \dot R \dotθ = 2bωω = 2bω^2$

Is this correct? is $(-\frac {π} {2} b ω^2)^2 = \frac {π^2} {4} b^2 ω^4$

 

[haruspex]

$a_R = \ddot R - R\dot θ^2 = -\frac {π} {2} b ω^2$ since $R = bθ = bπ/2$ and $\dot R = b\dot θ = bω$ and $\ddot R = b\ddot θ = 0$

$a_θ = R\ddotθ + 2 \dot R \dotθ = 2bωω = 2bω^2$

View attachment 211420

Is this correct? is $(-\frac {π} {2} b ω^2)^2 = \frac {π^2} {4} b^2 ω^4$

Looks right.