In order to relate the translational motion of the driving mass to the rotational motion of the rotating shaft (the disk-shaped part that the string winds around), we need to know r, the radius of the shaft. To do this, we are going to use a measuring device called a vernier calliper.

The caliper is like a simple ruler but in addition has a vernier scale on the sliding part that allows you to interpolate or measure accurately between millimeters. You should already be familiar with the vernier scale from your pre-lab. Here is a short description of how the ruler works. With the calipers set to the closed position, if you compare the millimeter scale to the vernier scale, you will see that the lower vernier scale has 50 divisions (10×5) compared to exactly 49 mm on the metric scale.  This means that every vernier scale division is 0.98 mm (49 mm/50), or is .02 mm less than a full mm. This 0.02 mm “phase shift” printed on the bottom right of the slider, is the resolution limit of this vernier calliper. So, with a relatively simple device, the resolution has been improved by 50 times that of a simple metric ruler.

PROCEDURE

Now let’s use the vernier calliper for what it was intended for, to give an accurate value of the rotating shaft’s radius, . You will determine this by measuring the diameter using the vernier calliper.

1.   Open the calliper arms (be careful, as the calliper slides open, a metal bit will stick out the end) and position the plastic wheel that is connected to the string between the caliper arms.

a.   Note: Make sure you are measuring the size of the part of the shaft that the string wraps around.

2.   Gently squeeze down on the wheel with the calliper arms. The ‘0’ mark on the sliding vernier scale is lined up between two marks on the fixed mm scale. The lower value of the mm scale gives the most significant digit(s) of the measurement.

3.   At some point, a vernier scale mark is exactly lined up with a mm scale mark. This vernier scale position determines the two least significant digits of the measurement.

a.   In this way, you will measure the diameter to the nearest hundredth of a millimeter (e.g., 22.12 mm), and then calculate the radius.

4.   Once you have determined the radius using the vernier callipers, record the value in the table of the Results section with uncertainty. Be sure to record the radius, not the diameter of the rotating shaft.