Falling thin rod and angular speed

[wondermoose]

Homework Statement

A 1.80 m long thing rod is balanced vertically on its tip on the floor. It starts to fall and its lower end does not slip. What is its angular speed just before it hits the floor?

Homework Equations

1/3ML^2
L=mvr

The Attempt at a Solution

When I first started this problem I had a better grasp, but as I started thinking about it I'm pretty sure I got further away. I started finding accelerations and velocities instead of getting back to the angular speed part of the problem. Now I'm trying to figure out how to actually do the problem. What is the first step?

Thanks.

 

[Hootenanny]

Homework Statement

A 1.80 m long thing rod is balanced vertically on its tip on the floor. It starts to fall and its lower end does not slip. What is its angular speed just before it hits the floor?

Homework Equations

1/3ML^2
L=mvr

The Attempt at a Solution

When I first started this problem I had a better grasp, but as I started thinking about it I'm pretty sure I got further away. I started finding accelerations and velocities instead of getting back to the angular speed part of the problem. Now I'm trying to figure out how to actually do the problem. What is the first step?

Thanks.

If the lower end does not slip, then you can treat it as a frictionless pivot. I would approach this problem using conservation of energy.

 

[wondermoose]

Can you explain that a little further? I attempted to use conservation energy, but apparently I'm missing something somewhere along the way and not doing the problem correctly at all. Am I going to find the total kinetic energy of the rod, maybe some kind of K(transitional) + K(rotational) equation?

Thanks

 

[Hootenanny]

Can you explain that a little further? I attempted to use conservation energy, but apparently I'm missing something somewhere along the way and not doing the problem correctly at all. Am I going to find the total kinetic energy of the rod, maybe some kind of K(transitional) + K(rotational) equation?

Thanks

At the beginning, just for the rod falls, what form is the energy in?

 

[rwisz]

I would approach this problem by first identifying the key variables and equations that are relevant. In this case, the key variables are the length of the rod, its mass, and its velocity. The relevant equations are the moment of inertia (1/3ML^2) and the angular momentum (L=mvr).

The first step would be to use the given information to calculate the moment of inertia of the rod. This will give us an idea of how difficult it will be to rotate the rod and therefore, its angular speed.

Next, we can use the conservation of angular momentum to solve for the angular speed just before the rod hits the floor. Since the rod is initially at rest and there are no external forces acting on it, the initial angular momentum is zero. Therefore, the final angular momentum must also be zero.

Using the equation L=mvr, we can set the final angular momentum equal to zero and solve for the angular speed. This will give us the angular speed just before the rod hits the floor.

I hope this helps. Remember to always start by identifying the key variables and equations and then use them to solve the problem step by step.