To find the average angular speeds for the rubber stopper with each set of washers, we'll use the formula for angular speed:
\[ \text{Angular speed} (\omega) = \frac{2\pi}{T} \]
Where:
- \( \omega \) is the angular speed (in radians per second).
- \( T \) is the period for one revolution (in seconds).
We already have the period for one revolution in the data table. We'll use this information to calculate the average angular speeds for each set of washers.
a. For 5 washers:
\[ \text{Angular speed} = \frac{2\pi}{29.73 \, \text{s}} \]
b. For 10 washers:
\[ \text{Angular speed} = \frac{2\pi}{23.83 \, \text{s}} \]
c. For 15 washers:
\[ \text{Angular speed} = \frac{2\pi}{19.805 \, \text{s}} \]
d. For 20 washers:
\[ \text{Angular speed} = \frac{2\pi}{16.345 \, \text{s}} \]
e. For 25 washers:
\[ \text{Angular speed} = \frac{2\pi}{15.335 \, \text{s}} \]
Now, let's calculate these values:
a. For 5 washers:
\[ \text{Angular speed} = \frac{2\pi}{29.73 \, \text{s}} \approx 0.211 \, \text{rad/s} \]
b. For 10 washers:
\[ \text{Angular speed} = \frac{2\pi}{23.83 \, \text{s}} \approx 0.263 \, \text{rad/s} \]
c. For 15 washers:
\[ \text{Angular speed} = \frac{2\pi}{19.805 \, \text{s}} \approx 0.318 \, \text{rad/s} \]
d. For 20 washers:
\[ \text{Angular speed} = \frac{2\pi}{16.345 \, \text{s}} \approx 0.385 \, \text{rad/s} \]
e. For 25 washers:
\[ \text{Angular speed} = \frac{2\pi}{15.335 \, \text{s}} \approx 0.410 \, \text{rad/s} \]
These are the average angular speeds for the rubber stopper with each set of washers.
