Analyzing Falling Rod Motion: Angular Velocity and Tip Speed

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The discussion focuses on a physics problem involving a long, thin rod pivoting at one end as it falls. The user successfully calculates the angular velocity of the rod upon hitting the table, using the moment of inertia formula I = (ML^2)/3 and energy conservation principles, resulting in an angular velocity of √(3g/L). However, they express uncertainty about determining the speed of the rod's tip, questioning whether it can be found by multiplying the angular velocity by the rod's length. The consensus confirms that this approach is correct, reinforcing the relationship between angular velocity and linear speed at the tip. The conversation highlights the importance of understanding rotational motion dynamics.
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Homework Statement


A long, thin rod of mass M and length L is standing straight up on a table. Its lower end rotates on a frictionless pivot. A very slight push causes the rod to fall over. As it hits the table, what are a)the angular velocity and b) the speed of the tip of the rod?

I'm having trouble visualizing this problem. If the rod it straight up and the lower end is rotating, isn't the top end also rotating. And I'm not sure how to approach this problem either.

Homework Equations





The Attempt at a Solution

 
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oh ok so i got that first part, finding the angular velocity when it hits the ground
used I= (ML^2)/3 because the axis of rotation is from one end of the rod, and then used energy to find that the angular velocity when it hits the table is square root of (3g/L)

But then for the second part of the question, the velocity of the top part of the rod, I'm not sure how to get. Would it just be the angular velocity I got from the first part multiplied by the length of the rod?
 
roman15 said:
Would it just be the angular velocity I got from the first part multiplied by the length of the rod?
Yep.
 

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