What Are the Absolute Velocity and Acceleration of a Collar on a Rotating Rod?

[CivilWork]

Homework Statement

http://www.lboro.ac.uk/faculty/eng/engtlsc/Eng_Mech/pastpapers/exam2001.pdf
Problem B6

Collar A slides along a horizontal rod that is rotating as shown in Figure Q.B6
with an angular velocity of 5 rad/s in the anti-clockwise direction. At a distance
of 200 mm from the axis of rotation of the rod, the collar has a velocity of 3 m/s
and an acceleration of 2 m/s2, both relative to the rod, in outward direction.
Determine the (absolute) velocity and acceleration of the collar at the instant
shown.
(figure in the upper link)

Homework Equations

The Attempt at a Solution

using Vr = r[dot]
and V(thetta) = r.thetta[dot]
and the corresponding equations for a(radial) and a(thetta)

But how to determine the values of r and its derivatives??

 

[Jhero]

Thank you for your question. To determine the values of r and its derivatives, we will need to use the information given in the problem. We know that the collar is located at a distance of 200 mm from the axis of rotation, so we can use this as the value for r. We also know that the collar has a velocity of 3 m/s and an acceleration of 2 m/s^2 relative to the rod. This means that the velocity and acceleration are measured with respect to the rod, not the axis of rotation.

To find the absolute velocity and acceleration, we will need to use the formula for relative velocity and acceleration, which is:

V(a) = V(b) + V(a/b)
a(a) = a(b) + a(a/b)

Where V(a) and a(a) are the absolute velocity and acceleration of point A, while V(b) and a(b) are the relative velocity and acceleration of point B. V(a/b) and a(a/b) are the velocity and acceleration of point A with respect to point B.

In this case, point A is the collar and point B is the axis of rotation. Using the given values, we can substitute them into the formulas and solve for the absolute velocity and acceleration of the collar at the given instant.

I hope this helps. Good luck with your problem!