Constrained Motion of a Pair of Rods

[Viraam]

Homework Statement

Homework Equations

$v = r \omega$

The Attempt at a Solution

Velocity of point B= $v_B = 4 \times \omega = 4$ m/s
Since the separation between B and C is constrained to be a constant, Velocity of B along rod = Velocity of C along the rod
$\Rightarrow v_B \cos \theta = v_C \cos \theta$
$v_B = v_C = 4$m/s

However the answer provided is $v_C = 4 \sqrt 3$ m/s. Where did I go wrong?

 

[TSny]

Please define which angle you are denoting by $\theta$.

Do the velocities of points B and C make the same angle with respect to rod BC?

 

[Viraam]

Please define which angle you are denoting by $\theta$.

Do the velocities of points B and C make the same angle with respect to rod BC?

Oops... Forgot to mention that. Sorry.

 

[TSny]

OK. But your red vector is not in the correct direction to represent the velocity of B.

 

[Viraam]

OK. But your red vector is not in the correct direction to represent the velocity of B.

Ohh I get it. I took the wrong vector. Isn't the red vector supposed to be tangential to AB?

 

[TSny]

Ohh I get it. I took the wrong vector. Isn't the red vector supposed to be tangential to AB?

$\vec {v}_ {_B}$ is not tangential to rod AB. Rod AB is rotating about A.

 

[Viraam]

$\vec {v}_ {_B}$ is not tangential to rod AB. Rod AB is rotating about A.

What is meant to ask is if the vector $\vec {v}_ {_B}$ at an angle of $90^ \circ$ to AB? Like in the figure here.

 

[TSny]

What is meant to ask is if the vector $\vec {v}_ {_B}$ at an angle of $90^ \circ$ to AB? Like in the figure here.

Yes. We would say the velocity is perpendicular to rod AB.

 

[Viraam]

Yes. We would say the velocity is perpendicular to rod AB.

Thanks. I got the right answer now. The angle between the velocity vector and the rod is $30^\circ$.
$v_B \cos 30^\circ = v_C \cos 60^\circ$
$v_C = 4 \sqrt3$

 

[TSny]

Looks good.