Dynamics: Angular Acceleration of Rods Connected to Disk

• vercingortix
BC and AB are attached by a pin and the dish OA has a constant angular velocity. The goal is to find the angular acceleration of bars BC and AB using the relative motion equations provided. The equations involve finding the velocity and acceleration of point B, which can be done by finding its x and y components as a function of the angle theta and then differentiating to get the velocity and acceleration.
vercingortix

Homework Statement

Bars BC and AB and dish OA are attached by a pin like in the picture. The dish has a constant angular velocity $\omega\_{0}$. Find the angular acceleration of bars BC and AB.

Homework Equations

Relative Motion Equations:
v$_{b}$=v$_{A}$+v$_{A/B}$
a$_{B}$=a$_{A}$+$\alpha_{A}$Xr$_{B/A}$-$\omega^{2}$r$_{B/A}$

The Attempt at a Solution

So far, I have this written down:

V$_{A}$=$\omega$r
a$_{A}$=V$_{A}$$^{2}$/r=$\omega^{2}$r

a$_{B}$=$\alpha_{BC}$Xr$_{BC}$-$\omega_{BC}^{2}$r$_{BC}$

Still just fumbling over these equations. Any help is appreciated.

Attachments

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welcome to pf!

hi vercingortix! welcome to pf!

(have a theta: θ and an omega: ω )

(centripetal acceleration is irrelevant)

ω = (vP - vQ)/PQ

so find vB as a function of θ

That equation looks foreign to me. What I'm currently trying to do is solve for angular acceleration of the bar by knowing the omega and accelerations of both A & B. Something like the second equation in my original post. I'm very lost.

hi vercingortix!

ω = |vP - vQ]/PQ

and

α = |aP - aQ|/PQ

are the definitions of angular speed and acceleration

so find the x,y components of B as a function of θ, and differentiate to get vB and aB

I would like to provide some guidance and suggestions for approaching this problem.

Firstly, it is important to understand the given scenario. We have a disk (dish) with a constant angular velocity, and two rods (BC and AB) attached to the disk by a pin. We are asked to find the angular acceleration of the rods.

To solve this problem, we can use the relative motion equations provided. These equations allow us to relate the motion of one object to the motion of another object. In this case, we can use the equations to relate the motion of the rods to the motion of the disk.

Next, we can apply the equations to each rod separately. For example, for rod BC, we can use the equation for acceleration (a_B) and substitute in the known values for the angular acceleration (alpha_BC) and angular velocity (omega_BC) of the disk, as well as the distance (r_BC) between the pin and the center of mass of rod BC. Similarly, we can do the same for rod AB.

It is also important to note that the angular acceleration of the rods will be different from that of the disk, as they are connected by a pin and will have different distances from the center of mass of the disk.

Lastly, it is always a good practice to check the units of the final answer to ensure they are consistent with what is expected for angular acceleration (rad/s^2).

Overall, this is a problem that requires careful application of the equations and understanding of the given scenario. With practice and a solid understanding of the concepts, you will be able to solve similar problems with ease.

1. What is angular acceleration?

Angular acceleration is a measure of how quickly the angular velocity of an object changes over time. It is represented by the symbol "α" and is measured in radians per second squared.

2. How is angular acceleration related to linear acceleration?

Angular acceleration and linear acceleration are related through the equation α = a/r, where "a" is linear acceleration and "r" is the radius of the rotating object. This means that for a given linear acceleration, a smaller radius will result in a larger angular acceleration.

3. How do you calculate the moment of inertia for a rod connected to a disk?

The moment of inertia for a rod connected to a disk can be calculated by adding the individual moments of inertia for each object. For a rod, the moment of inertia is 1/12 * m * L^2, where "m" is the mass of the rod and "L" is the length. For a disk, the moment of inertia is 1/2 * m * r^2, where "m" is the mass and "r" is the radius. Add these two values together to get the total moment of inertia.

4. How does the distribution of mass affect angular acceleration?

The distribution of mass directly affects the moment of inertia, which in turn affects the angular acceleration. Objects with a larger moment of inertia will have a smaller angular acceleration, while objects with a smaller moment of inertia will have a larger angular acceleration.

5. Does the angle of the rod affect the angular acceleration?

Yes, the angle of the rod can affect the angular acceleration. The moment of inertia for a rod depends on the axis of rotation, so changing the angle of the rod can change the moment of inertia and therefore the angular acceleration. Additionally, changing the angle can also affect the direction of the angular acceleration.

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