(2) The angular acceleration of the roll while it is falling in radians/s/s.
(3) The translational acceleration of the center-of-mass of the roll in m/s/s.
(4) The final translation speed of the roll in m/s.
(5) Using a free-body diagram and Newton's Second Law of Motion as well as the mass of the combined TP roll and PocketLab, compute the tension in the sheets while the roll is falling.
1. What is the yo-yo doing at the points labeled with green dots?
2. What is the yo-yo doing at the points labeled with red dots?
3. In contrast to the green dots, what has caused the horizontal lines which have been labeled with the letter A?
4. What is the yo-yo doing on the lines labeled with the letter B?
5. What is the yo-yo doing on the lines labeled with the letter C?
6. Can you think of a way to determine the actual maximum angular velocities where you see the horizontal lines labeled A?
2. Why is there a sort of sine wave feature in angular velocity from points A to B, and from points C to D?
3. What is the angular velocity of the wheels and axle system just before making contact with the table top?
4. What is the speed of the center-of-mass of the system just before making contact with the table top?
5. What is the angular velocity of the wheels and axle system at point C?
6. What is the speed of the center-of-mass of the system at point C?
7. Explain the physics of why the speed of the center-of-mass of the system increased upon contacting the table top.
PocketLab in conjunction with a 33-45-78 RPM turntable is an ideal setup for studying centripetal acceleration. There are two videos that can be found in the Videos page of this web site. They show that (1) keeping radius constant implies that centripetal acceleration is proportional to the square of the velocity, (2) keeping velocity constant while varying the radius implies that centripetal acceleration is inversely proportional to the radius.
The PocketLab is placed in its silicone protective case to provide greater friction so that it doesn't slide off the turntable. Y is toward the center of the turntable, and X is in the direction of rotational motion of the turntable. Single-graph mode is used with acceleration selected to be graphed.
From the accel X data in the videos students can then use Excel, Google Sheets, or any other analysis software to make graphs of (1) accel X vs. velocity-squared, and (2) accel X vs. the reciprocal of the radius. Both of the graphs should be pretty close to straight lines, giving support for the desired outcomes.