Rotation of a meterstick

We start with a meterstick -- one of the metersticks in the classroom. It has length L = 1.00 m and mass M = 0.150 kg; we will assume that the density is uniform.

The stick has a number of holes drilled in it, so that the stick can be suspended and rotated around some point a distance x from the center of the stick.

What is the moment of inertia of the meterstick for x = 0.20 m?

I will set up the meterstick so that it is originally horizontal, then release it. It will swing down, up on the other side, then back down, etc.

Let us begin in a generic sense ...

Write a formula which shows the torque on the meterstick when it is an angle theta from the bottom of its swing.
Write a formula which shows the angular acceleration of the meterstick when it is an angle theta from the bottom of its swing.

If you have time ...

Suppose that the meterstick is moved to initial angle theta_max and then released from rest. Write a formula which shows the angular velocity of the meterstick when it is at the bottom of its swing. (Hint: it's easier to use energy than torque in this case...)

Now, let's get specific. For this particular meterstick, make a table and a graph.

make a table showing the angular acceleration (in radians/sec) of the meterstick at angles theta = 0, 0.10, 0.20, 0.30, 0.60, 0.9, 1.2, 1.5 radians.
make a graph which shows angular acceleration (in rad/sec^2) versus angular displacement (in rad), over the range theta = -1.5 to +1.5 radians. Plot the points from your table.

If you have time ...

compute the maximum angular velocity of the stick if it is released from initial position theta_max = 0.20 radians

Look at your graph to answer these two questions.

Is the angular acceleration always linearly related to the angular displacement, or only over a limited range?
Write an equation of the form
```
            ang accel  =   (const)  *  (ang displacement)

   
```
Use your graph to find the value of the constant. What are its units?