Calculating Angular and Relative Velocities in a Slider-Rod System

[FChebli]

1. Homework Statement :

Rod BP (20 degrees from horizontal) attached at slider P on rod AD (60 degrees from horizontal), distance between 2 rods = 300 mm, wA = 10 rad/s
(I) Find angular velocity of rod attached at B
(II) Find relative velocity of slider P with respect to the rod on which ot slides.

2. Homework Equations :

v = w r

3. The Attempt at a Solution :

Using the sines rule: BP = 404 mm, AP = 160 mm
vP = 0.16 x 10 = 1.6 m/s

How do I know the directions of vp, vp' and vp/p'?
Is there a specific rule for the direction of vp/p'? Does it have to be perpindiculer to one of the rods?

Thank you!

 

[KataKoniK]

Thank you for your question. I am happy to help you find the answers you are looking for. To start, let's break down the problem and look at each part separately.

For part (I), we can use the equation v = w r to find the angular velocity of the rod attached at B. We know the distance between the two rods (300 mm) and the angular velocity of rod AD (10 rad/s). Using the sines rule, we can find the length of BP (404 mm) and AP (160 mm). Then, using the equation v = w r, we can find the angular velocity of the rod at B by substituting in the values we have calculated.

For part (II), we can use the same equation v = w r to find the relative velocity of slider P with respect to the rod on which it slides. We know the angular velocity of rod AD (10 rad/s) and the distance between the two rods (300 mm). Using the sines rule, we can find the length of BP (404 mm) and AP (160 mm). Then, using the equation v = w r, we can find the relative velocity of slider P by substituting in the values we have calculated.

As for the direction of vP, vP', and vP/P', we can use the right-hand rule to determine the direction of the velocity vector. Simply point your right thumb in the direction of the angular velocity (w) and curl your fingers towards the direction of the radius (r). The direction your fingers point in is the direction of the velocity vector.

I hope this helps answer your question. If you have any further questions, please don't hesitate to ask. Keep up the good work!