Calculate the Initial Calue of the Force at the Bearing

AI Thread Summary
The discussion focuses on calculating the initial force exerted by a bearing on a uniform slender bar pivoted and released from a horizontal position. The user initially expresses uncertainty about how to approach the problem but later derives the angular acceleration using the equation ƩMO = IGα = -mg(L/2). They establish a normal and tangential coordinate system to analyze forces, leading to the equation ƩFt: mrα = Oy - mg. By substituting the expression for α into this equation, they determine the initial force at the bearing to be 88.29 N. The thread highlights the importance of applying rotational dynamics and force analysis in solving the problem.
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Homework Statement



The uniform slender bar is pivoted at and swings freely in the vertical plane. If the bar is released from rest in the horizontal position, calculate the initial value of the force exerted by the bearing on the bar an instant after release.

I have attached an image of the question


Homework Equations





The Attempt at a Solution



I'm honestly not sure how to start this question. I'm pretty sure that this is a straightforward question

I think I may need to use the equation:

ƩMO = IGα + maGd

Any advice would be appreciated. Thank you
 

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Ahh, wait I've figure it out now.

I used the fact that:

ƩMO: IGα = -mg(L/2)

Solving for α = -mg(0.5L)/IG

where L is the length of the bar

Then I applied a normal and tangential coordinate system, with t pointing downwards and n pointing towards O.

ƩFt: mrα = Oy - mg

Plugging in the formula that I solved for α above I get

Oy = mr[-mg(0.5L)/Ig] + mg

My final answer was 88.29 N
 

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