Setting Up a Circular Motion Lab and Grading It

The lab itself is usually straightforward. You spin a stopper on a string through a tube with weights hanging from the other end. The centripetal force comes from the hanging mass, the radius is set by the marker distance, and you time how long it takes for a certain number of revolutions. The answer key that follows is pretty standard across most AP Physics and introductory college courses.

Where to Find a Circular Motion Lab Answer Key

Search results will give you several versions. The CBSE Class 11 physics circular motion lab answer key tends to focus on the conical pendulum setup. Some versions use a rotary motion sensor. The data analysis differs slightly depending on what your school has. Most teachers share theirs through document hubs or internal LMS pages rather than public forums. I have used two setups over the years. The string-and-stopper version is more common but introduces friction at the tube entrance. That friction is usually the reason students get percent errors around 12 to 25 percent instead of the textbook ideal. I started applying a correction factor of roughly 0.97 to the hanging mass reading to compensate. That brought my class averages down to about 4 to 6 percent error consistently.

Expected Results and Calculations

The core equation is F_c equals m times v squared over r. With the hanging mass providing the centripetal force, you substitute m_hanging times g for F_c. The velocity comes from the circumference times the number of revolutions divided by the period. Most students mess up the unit conversion on the radius. They measure in centimeters and forget to convert to meters before plugging into the formula. That single mistake skews every result downstream. For the theoretical part, expected answers look like this: - Tension in the string approximates the weight of the hanging mass - Centripetal acceleration equals angular velocity squared times radius - Period should remain constant regardless of the stopper mass as long as the hanging mass stays the same I remember one student who got a period of 0.85 seconds with a radius of 0.50 meters and a hanging mass of 0.10 kg. The calculation gave an expected centripetal force of about 0.98 newtons. When she measured the actual force from the hanging mass, it came out to 1.05 newtons. She traced the discrepancy back to the string stretching slightly under load. The unstretched length was about 3 centimeters shorter than the marked radius. That length change was enough to shift her entire data set.

Common Pitfalls and Edge Cases

The radius changes when the hanging mass changes. Students often set the radius, then swap out masses without remeasuring. That invalidates every calculation after that point. The proper sequence is to set the radius first, then adjust the hanging mass, then verify the radius has not shifted. Friction at the tube is another issue. The string drags against the plastic as it passes through. I used a small bead of silicone grease at the entrance point. That cut the friction from about 0.15 newtons to roughly 0.03 newtons. The improvement was noticeable immediately in the consistency of the period readings. Air resistance matters more than most people account for. At higher speeds, the stopper experiences drag proportional to velocity squared. For a plastic washers as the rotating mass, this effect becomes measurable above about 15 revolutions per second. The period drifts upward gradually as the speed decreases. Students sometimes attribute this to measurement error when it is actually just drag slowing the system.

Grading Considerations

When using a Circular Motion Lab Answer Key, allow for a reasonable error band. Anything within 10 percent of the expected value is typically acceptable for this type of experiment. The setup is inherently imprecise due to friction, air resistance, and the difficulty of maintaining a constant radius while timing. Results that fall outside that range usually indicate a procedural error rather than a calculation mistake. Some schools use a rotary motion sensor instead of the string method. That approach eliminates friction issues entirely and provides real-time velocity data. The trade-off is equipment cost and calibration time. A standard PASCO rotary motion sensor costs around 300 dollars and requires a smart interface and software license. For schools without that budget, the string method remains viable with careful attention to the sources of error.

Data Analysis Steps

Record the radius in meters, the hanging mass in kilograms, and the period in seconds. Calculate velocity as two pi r divided by t. Compute centripetal force as the test mass times velocity squared divided by radius. Compare that to the hanging mass times gravitational acceleration. The percent difference tells you how well the theory matches the experiment. A typical data table looks like this: | Radius (m) | Hanging Mass (kg) | Time for 10 rev (s) | Period (s) | Velocity (m/s) | F_c (N) | F_hang (N) | % Diff | |------------|-------------------|---------------------|------------|----------------|---------|------------|--------| | 0.50 | 0.10 | 7.0 | 0.70 | 2.24 | 0.50 | 0.98 | 49 | | 0.40 | 0.10 | 6.2 | 0.62 | 2.04 | 0.43 | 0.98 | 56 | | 0.30 | 0.10 | 5.4 | 0.54 | 1.75 | 0.34 | 0.98 | 65 | The percent difference column shows the comparison between calculated centripetal force and the hanging weight. Values above 50 percent usually indicate a systematic error. Check the radius measurement, the timing, and whether the radius stayed constant throughout the trial.

Lab Procedure Summary

Set up the apparatus. Attach the stopper to one end of the string. Thread the string through the tube. Tie the hanging mass to the other end. Mark the radius point on the string. Begin spinning the stopper horizontally. Adjust the speed until the marker stays at the reference point. Have a partner time 10 complete revolutions. Record the total time. Repeat for different radii or hanging masses as required. The entire process takes about 20 to 30 minutes for a complete data set with three or four trials. Data collection is usually the fastest part. The calculations and error analysis take longer, especially when students are learning to apply the formulas correctly. Budget sufficient time for both parts of the lab session.