Dynamics: Rigid body problem, angular rotation

[student13]

Homework Statement

An L-shaped plate is pinned at a point F and G with two poles OF and ED (OF = 1m, OG = 0.6m), which in turn are pinned at fixed points O and E, respectively, as shown in the attached image. If rod OF rotates with a constant angular velocity 0.2rad/s counter-clockwise, when the mechanism passes the position as show, determine
i) the angular velocity of the L-shaped plate
ii) the instantaneous zero velocity centre
iii) the angular acceleration

Homework Equations

omega = velocity x distance

The Attempt at a Solution

using trig, the length FG = 3 m, therefore, the velocity of F can be calculated using w = v/r = w(OF) = v(F) / OF => v(F) = 0.2 m/s,

however, i do not understand as how can V = W, and then how do i go on to find the angular velocity of the L-shaped plate? i am so confused. please help me, rather than tell me what or how to do something, thank you

 

[KataKoniK]

Dear fellow scientist,

Thank you for your post. It seems like you are on the right track with your calculations so far. To find the angular velocity of the L-shaped plate, you can use the equation w = v/r = w(OF) = v(F) / OF. In this case, v(F) is the velocity of point F, which you have already calculated to be 0.2 m/s. Now, to find the angular velocity of the L-shaped plate, you need to find the distance from point F to the pivot point O. This distance can be calculated using trigonometry, as you have mentioned, and is equal to 3.2 m. Therefore, the angular velocity of the L-shaped plate is 0.0625 rad/s (0.2/3.2).

Moving on to the instantaneous zero velocity centre, this is the point on the mechanism that has zero velocity at any given instant. In this case, it is the point where the velocity of point F is equal to the velocity of point G. Using the equation v(F) = v(G) = w(FG) x r(FG), we can calculate the distance from point F to the instantaneous zero velocity centre. This distance is equal to 1.2 m, which is also the distance from point G to the instantaneous zero velocity centre.

Lastly, to find the angular acceleration, we can use the equation a = alpha x r, where alpha is the angular acceleration and r is the distance from the pivot point to the point of interest. In this case, we can use the distance from point F to find the angular acceleration, which is equal to 0.025 rad/s^2 (0.2/8).

I hope this helps clarify the steps you need to take to solve this problem. Let me know if you have any further questions.