relationship between angular speed (ω) and angle of the string above the vertical (θ) for a particular rotating apparatus

relationship between angular speed (ω) and angle of the string 

above the vertical (θ) for a particular rotating apparatus

Purpose:

Through modeling the circular motion with different angular speed, to find the relationship between angular speed (ω) and angle of  the string above the vertical (θ) for a particular rotating  apparatus.

Equipment:

Tripod, rod, string, mass, meter stick, timer

Experiment:

1. Set up tripod with a rod horizontally at the top of tripod, attach a string to one end of the rod with a mass on the other end.

2. Measure the height of the tripod h=211 cm and the length of the rod l=61.5 cm.

3. Measure the time of 10 rotations.

4. Measure the height of the hanging  mass h2 (with a certain angle) by slowly raising a piece of paper, which was attached to a sturdy pole.

5. Repeat step 3 and 4 with different angular speed.

Data:

1) 37 sec. and 49 cm.

2) 30 sec. and 72 cm.

3) 26 sec. and 92 cm.

4) 25 sec. and 104.5 cm.

5) 23 sec. and 119 cm.

6) 21 sec. and 132 cm.

7) 19 sec. and 147 cm.

8) 17 sec. and 157 cm.

Data analysis:

1. Divide the time by ten to get the period T.

2. Calculate the angel θ by height of the tripod h , the height of the mass h2, and the length of the string l.

3. Open an excel and input the data of period T, the height of the mass h2, and the angel θ.

4. In Cell D2, input the formula for calculated angular speed ω in terms of g, θ, d, and l.
5. In Cell E2, input the formula for measured angular speed ω in terms of T.
6. Drag down the column and get the calculated angular speed ω and measured angular speed ω for all other experiments.
7. Copy the column of calculated angular speed ω and measured angular speed ω, and paste it in Logger Pro.
8. Click Linear Fit to get the graph and equation between calculated angular speed ω and measured angular speed ω.

Result:

Conclusion:

We find the relationship between angular speed (ω) and angle of  the string above the vertical (θ) for a particular rotating apparatus. And we verify it through ω=2pi/T.