What Is the Correct Method to Calculate W and Alpha in Planar Kinematics?

[smruthi92]

pls see attached file.

so i thought i could use this eqn:

a_A = w² AO e_n + alpha AO e_t

but when i try to work out w, something goes wrong. i do:

w = 7.16605 (normal velocity i found by having the given velocity as a y coordinate one, then resolving for normal/tangential) / 0.25. but this itself is wrong. what have i done? also how do i calculate alpha? i have no IDEA how to do it!

thanks a lot for ur help,
cheers,
s.

 

[omoplata]

alpha is the angular acceleration, or the rate of change of w w.r.t. time.

Tell me if you get stuck.

 

[smruthi92]

yeh but how do i calculate it with the data given? we haven't been given an equation to differentiate to find alpha. also I am still stuck on calculating w.

 

[omoplata]

w is the angular velocity, or the rate of change of theta w.r.t time.

If you find w as a function of theta you can differentiate w.r.t time.

You can find w as a function of theta by considering the component of the linear velocity of the pin which is perpendicular to AO.

 

[rwisz]

It seems like you are on the right track with using the equation aA = w2 AO en + alpha AO et to solve for w and alpha. However, it is important to make sure that you are using the correct values for each variable. It is possible that you may have made a mistake in your calculations or used the wrong values for the velocity and normal/tangential components.

To calculate w, you will need to use the normal component of the velocity (in this case, 7.16605) and the distance between the point of interest and the axis of rotation (0.25). So the correct equation would be w = v_n / r. Make sure to double check your calculations to ensure that you are using the correct values and units.

To calculate alpha, you will need to use the tangential component of the acceleration (aT) and the distance between the point of interest and the axis of rotation (0.25). The equation for alpha would be alpha = aT / r. Again, make sure to use the correct values and units in your calculations.

If you are still having trouble, it may be helpful to review the concepts of planar kinematics and the equations used to solve for different variables. You can also consult with a colleague or your instructor for further assistance. Good luck!