The question
Name: ______________________ Date: ____________ Measuring a platform’s rotational inertia (10 points)
Experimental setup
Measuring a platform’s rotational inertia
Students want to find the rotational inertia I of a horizontal platform that turns on a vertical axle. A light string is wound on a small spool of radius r = 0.020 m fixed to the axle, runs horizontally over a light, frictionless pulley and holds a hanging mass m. When the mass is released from rest, it falls and the platform spins up. The string does not slip on the spool.
For a hanging mass m falling with acceleration a, the tension in the string is m(g − a), and the spool’s radius links a to the platform’s angular acceleration. The students’ results (use g = 9.8 m/s²):
| Hanging mass m (kg) | Fall time t (s) | Acceleration a (m/s²) | m(g − a) (N) |
|---|---|---|---|
| 0.050 | 7.26 | 0.0304 | 0.488 |
| 0.100 | 4.76 | 0.0706 | 0.973 |
| 0.150 | 3.87 | 0.1068 | 1.454 |
| 0.200 | 3.28 | 0.1487 | 1.930 |
| 0.250 | 2.96 | 0.1826 | 2.404 |
(a) Describe a procedure the students could use to collect the data in the table. Include the measurements they make, the equipment for each, and one way to reduce experimental uncertainty. [3 points]
(b) Describe what quantities the students should plot to obtain a straight line whose slope can be used to find I, and explain how they would find I from the slope. [2 points]
(c) On the grid provided, plot the data needed to make the graph you described in part (b). Label the axes with quantities and units, use a linear scale, and draw a best-fit line. [3 points]
(d) Calculate the rotational inertia of the platform, using the slope of your best-fit line. [2 points]