Quick answer: Uniform circular motion is travel at constant speed along a circle. This AP Physics 1 lab on centripetal acceleration gives the aim, the equipment, the safety points, a step-by-step method, sample results and 7 analysis questions; the answers are on a separate page and the lab sheet is a free printable PDF.
A hanging weight supplies the tension that keeps a bung moving on a circle. By changing the weight and timing the revolutions, you test whether the centripetal force is proportional to 1/T² and measure the gradient predicted by 4π² m r.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 2
Aim
Test how the centripetal force on a bung depends on its period of rotation, by balancing the tension with a hanging weight.
Equipment
- Rubber bung of mass 25 g tied to 1.5 m of string
- Smooth glass tube, length 15 cm, with taped ends
- Slotted masses (50 g to 250 g) and a hanger
- Stopwatch, metre rule, balance, adhesive tape marker
Safety
Wear goggles and swing the bung in a clear space away from other people. Keep the hanging masses over a soft surface and check the knots before every run. Tie the string to the bung with a secure knot.
Method
- Weigh the bung. Pass the string through the tube, attach the hanger below, and mark a point 0.60 m from the bung with the tape.
- Hang a mass M = 0.050 kg. Hold the tube vertically and whirl the bung in a horizontal circle so that the marker stays just below the tube.
- Keep the radius constant. Time 20 revolutions with the stopwatch and record the time.
- Repeat with M = 0.100, 0.150, 0.200 and 0.250 kg.
- Calculate F = M g, the period T and 1 / T² for each row.
Results
Sample measurements (bung mass 0.025 kg, radius 0.60 m, g = 9.81 N/kg):
| Hanging mass M (kg) | Force F = Mg (N) | Time for 20 revolutions (s) | Period T (s) | 1/T² (s⁻²) |
|---|---|---|---|---|
| 0.050 | 0.49 | 22.1 | 1.105 | 0.82 |
| 0.100 | 0.98 | 15.5 | 0.775 | 1.66 |
| 0.150 | 1.47 | 12.8 | 0.640 | 2.44 |
| 0.200 | 1.96 | 11.0 | 0.550 | 3.31 |
| 0.250 | 2.45 | 9.8 | 0.490 | 4.16 |
Analysis questions
Question 1 Completing a row
Show how the entries in the row for M = 0.150 kg were obtained.Question 2 Drawing the graph
Plot F (vertical axis) against 1 / T² (horizontal axis) and draw the best-fit line. Describe the shape.Question 3 Using the gradient
Calculate the gradient of the line and compare it with the theoretical value 4π² m r.Question 4 Timing uncertainty
The stopwatch reading for 20 revolutions is uncertain by ±0.3 s. Find the percentage uncertainty in 1/T² for M = 0.200 kg.Question 5 Effect of a sagging string
The string sags slightly instead of being level. Explain the effect on the gradient.Question 6 Radius doubled
Predict the new gradient if the experiment is repeated with r = 1.20 m and the same bung.Question 7 Improvements
Suggest two improvements that would reduce random errors.
