The method and the results are on the centripetal acceleration lab. Do the analysis yourself first, then check the answers below.
Quick answer: Uniform circular motion is travel at constant speed along a circle. These answers go with the AP Physics 1 lab on centripetal acceleration: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
The sample data follow the theory closely. These model answers show the calculations, the expected graph and the main sources of error for the lab.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 2
F = M g = 0.150 × 9.81 = 1.47 N. T = 12.8 ÷ 20 = 0.640 s. 1/T² = 1 ÷ 0.640² = 1 ÷ 0.4096 = 2.44 s⁻².
Question 2 Drawing the graph
The five points lie close to a straight line through the origin. F is directly proportional to 1/T².
Question 3 Using the gradient
Using the line through the origin, gradient = ΣF·x ÷ Σx² = 0.593 N s². Theory: 4π² × 0.025 × 0.60 = 0.592 N s². The difference is +0.1 %, so the data agree with the theory.
Question 4 Timing uncertainty
Percentage uncertainty in the time = 0.3 ÷ 11.0 = 2.7 %. Since 1/T² depends on T squared, double it: about 5.5 %.
Question 5 Effect of a sagging string
The tension acts at a small angle above the horizontal, so only its horizontal component provides the centripetal force. Mg then overestimates the real centripetal force, so the plotted F is too large for each period and the gradient comes out slightly too high.
Question 6 Radius doubled
Gradient = 4π² m r is proportional to r, so doubling r doubles it: 4π² × 0.025 × 1.20 = 1.18 N s².
Question 7 Improvements
Time 30 revolutions and repeat each run three times so the percentage timing uncertainty falls; use a video with a frame-by-frame count to find the period more accurately. Longer timed runs and repeats.
