Circular Motion

The question behind the experiment

Constant speed does not guarantee zero acceleration. An object following a circle continuously changes its velocity direction, requiring an inward net force. This course connects that statement to force-sensor and timing measurements in rotating setups. Identify the center of the path before drawing an acceleration arrow. The question is which actual interactions provide the inward net force, and how much force is required for a chosen mass, radius, and speed in the modeled apparatus.

Plan a useful comparison

Change speed while keeping the rotating mass and radius fixed. Record the force and the measured period rather than relying on the turntable's visual appearance. Convert period to speed using the path length for a complete revolution. Plot force against speed and against squared speed to compare the functional relationships. An inward force that grows rapidly with speed is not evidence of a new type of force; it is a consequence of the changing acceleration required by the path.

Connect the observation to the model

Draw the real forces for each setup. A string's tension, static friction, or components of normal force and gravity can supply the inward resultant, depending on the apparatus. Do not add a separate centripetal force arrow on top of those forces. The term describes the radial role of the net force. If the inward constraint disappears, predict the immediate direction of travel from the velocity tangent, rather than drawing an outward radial launch from the circle.

Interpret the result carefully

The conical-pendulum investigation adds a vertical force balance to the radial motion. Its string tension has different components in those directions. Use the geometry to relate the height below the support to the period, then compare that prediction with timing data. A faster rotation changes the cone geometry as well as the path radius. Keep those quantities together when explaining why a pendulum rotating faster can complete a revolution in less time despite tracing a wider circle.

Build an explanation from your evidence

A swinging pendulum is another case where sensor tension and the inward net force must be distinguished. At a low point, gravity still acts, and the tension can exceed the weight because their difference supports radial acceleration. Compare the force reading with a free-body calculation for the same position. The experiment therefore tests force accounting as well as speed dependence. Report rounded readings as measurements and reserve full-precision values for checks of the specified ideal model.

A reference case from this course

In the matched Ideal turntable comparison with mass 0.250 kg and radius 0.16 m, the displayed force changes from 0.89 N at 45 rpm to 3.55 N at 90 rpm. The rounded readings give a force ratio near four when speed doubles. Keep mass and radius fixed for that interpretation.

Keep the investigation reproducible

Before changing the setup, write a prediction that names the measured quantity and the expected direction of change. Retain the original trial as a reference. Record the apparatus conditions, units, and whether you used Ideal or Real lab mode. If the selected activity includes seeded variation, keep the seed and run identity with the result so another comparison does not silently mix different conditions.

Separate the observation from its explanation. A reading or a counted object belongs in the evidence; the relationship you use to interpret it belongs in the reasoning. When a result differs from the reference case, check the settings and measurement procedure before deciding that the model relationship has failed. Describe a specific source of uncertainty and where it enters your calculation. Finish with a claim supported by the recorded comparison, and identify an additional trial that could distinguish your explanation from an alternative.

Continue the comparison

Explore force balance in Torque & Balance and periodic motion in Pendulum & Spring Oscillations. Distinguish a rotational equilibrium condition from the nonzero inward net force required by a moving circular path.