(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A thin rod of length L stands vertically on a table. The rod begins to fall, but its lower end does no slide. (a) Determine the angular velocity of the rod as a function of the angle [tex]\phi[/tex] it makes with the tabletop. (b) What is the speed of the tip of the rod just before it strikes the table?

2. Relevant equations

1) Torque = Moment of Inertia * angular acceleration

T = I * [tex]\alpha[/tex]

T = Fdsin[tex]\phi[/tex]

3. The attempt at a solution

I am not sure if this is the correct solution because I'm not sure if I'm thinking about the problem correctly.

We know there is a force from gravity Fg. It will depend on the angle of the rod with the table. This relation is given by Fg([tex]\phi[/tex]) = mgsin[tex]\phi[/tex].

so T([tex]\phi[/tex]) = mgsin[tex]\phi[/tex]d = mg(L/2)sin[tex]\phi[/tex].

now [tex]\alpha[/tex] = [tex]\frac{T}{I}[/tex], so

[tex]\alpha[/tex]([tex]\phi[/tex]) = (mgLsin[tex]\phi[/tex])/2I,

and we know I for a rod in this case is 1/3mL^2

so [tex]\alpha[/tex]([tex]\phi[/tex]) = [tex]\frac{3gsin\phi}{2L}[/tex]])

then I integrate the ang. acceleration to find the angular velocity from [tex]\pi[/tex]/2 to 0.

I found [tex]\omega[/tex] = [tex]\frac{3g}{2L}[/tex] rad/sec .

I have good feeling I am leaving something out in this solution, such as possibly something to do with friction with the surface. I have a feeling the words "falls without slipping" mean something I am not realizing.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Rotational Motion Problem

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