Vertical Component Reactions given angular velocity

In summary, the problem involves a pendulum consisting of a disk of mass M1 and a slender rod of M2. The components of reaction that the pin O exerts on the rod at the horizontal position, with an angular velocity of ω, need to be determined. Using the equations for moment of inertia and the period of the pendulum, the solution attempted involved taking the moment from point O and calculating the moment of inertia. However, further steps are needed to find a complete solution.
  • #1
SteliosVas
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Homework Statement



A pendulum consists of a disk of mass M1, and a slender rod of M2 (which happens to be 0kg),.

Determine the components of reaction that the pin O, exerts on the rod just as it passes the horizontal postion, at which time its angular velocity is ω.

Know we know M1 = 15kg
a which is radius of disk is 0.25m
Rod is 1m
=8rads/s
g= 9.81m/s2

Homework Equations



Well

I of rod=1/12 ML^2
I of disk=1/4 MR^2+ 1/12 ML^2
I=Icom + Mh^2
T=2pi sqrt(I/Mgh)

Now i don't know how I can fit in the angular velocity into this..

The Attempt at a Solution



Well I tried taking the moment from point O, and got 15*9.81 = 147.15N.
I got the moment of inertia = 23.67kgm^2

After that I am lost :(

I have attached a picture, if that might help.

THese problems are taking out of my dynamics textbook :/
 

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  • #2
Hi!

I would assume it has to do something to do with the mass of the pendulum and the centripetal acceleration that the disk has due to its rotation. The force due to the rotation would be m*Omega^2*r. What about summing the force due to gravity and the one due to the centripetal acceleration? I hope this helps.
 

FAQ: Vertical Component Reactions given angular velocity

What is the vertical component reaction in a rotating system?

The vertical component reaction is the force exerted in the upward or downward direction on an object in a rotating system due to the object's angular velocity. It is a result of the object's inertia and the centripetal force acting on it.

How is the vertical component reaction calculated?

The vertical component reaction can be calculated using the formula Rv = mrω², where Rv is the vertical component reaction, m is the mass of the object, r is the distance from the center of rotation to the object, and ω is the angular velocity of the object.

What is the direction of the vertical component reaction?

The direction of the vertical component reaction depends on the direction of the object's angular velocity. If the object is rotating clockwise, the vertical component reaction will be in the downward direction. If the object is rotating counterclockwise, the vertical component reaction will be in the upward direction.

How does the vertical component reaction affect the stability of a rotating object?

The vertical component reaction plays a crucial role in maintaining the stability of a rotating object. If the vertical component reaction is not balanced by other forces, the object may experience a torque and become unstable. Therefore, it is important to consider the vertical component reaction when designing rotating systems.

Can the vertical component reaction be affected by changing the object's angular velocity?

Yes, the vertical component reaction is directly proportional to the object's angular velocity. This means that if the angular velocity increases, the vertical component reaction will also increase, and vice versa. This relationship is described by the formula Rv ∝ ω².

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