This experiment is designed for AP Physics and college physics students. It considers a solid cylinder of mass M and radius R that is rolling down an incline with a height h without slipping. Using energy and dynamics concepts, students first derive equations for (1) the speed of the center of mass of the cylinder upon reaching the bottom of the incline, and (2) the acceleration of the center of mass of the cylinder as it rolls down the incline. The free-body diagram at the center shows all forces acting on the cylinder as it rolls down the incline.
Then students use PocketLab and the VelocityLab app to perform an experiment that verifies their two equations.
The photo below shows the experiment setup as performed by the author. An unopened jellied cranberry sauce can is used as the cylinder. A cranberry sauce can was selected as there is virtually no sloshing of the cranberry sauce as the can rolls down the incline, and the end of the can was a perfect size for mounting PocketLab using Velcro. A plastic drafting triangle was used to hold the can still and then release it at the top of the ramp. A pillow was used as a bumper at the bottom of the ramp to stop the can after reaching the bottom.
The movie below shows video combined with data for a typical run in which the radius of the cylinder was 7.4 cm and the height of the ramp was 10.2 cm.
The figure below shows graphs of position, speed, and acceleration obtained by using Excel to massage the data in the pos_vel_acc.csv file produced by VelocityLab. The position graph shows the region in which the cylinder is rolling down the incline. The position graph also indicates the length (1.164 m) of the inclined plane. The speed graph shows that the speed at the bottom of the incline is 1.115 m/s. The slope of the region where the cylinder is rolling down indicates the acceleration (0.580 m/s/s). The acceleration can also be obtained directly from the acceleration graph by averaging the acceleration points (0.589 m/s/s) during the time that the cylinder is rolling down the incline. Both methods for determining the acceleration obtain close to the same value.
The theoretical equation for the speed at the bottom of the incline predicts that the speed should be 1.155 m/s. Our experimental value of 1.115 m/s represents an error of only 3.6%. The theoretical equation for the acceleration of the center of mass as the cylinder rolls down the incline predicts that it should be 0.572 m/s/s. Our experimental value of 0.585 (averaging the value from slope of speed graph and mean from the acceleration graph) represents an error of only 2.3%.
The teacher is encouraged to view the attached pdf file that provides the theoretical equations and their derivations.
