An experiment is performed to measure the moment of inertia of a thin
PHYSICS · Multi-part · CBSE · Physics · Magnetism and Matter · Magnetism and Matter
Problem
An experiment is performed to measure the moment of inertia of a thin, uniform ring. The ring is mounted so that it can rotate freely about its central axis. The measured rotational kinetic energy and angular speed for six trials are recorded along with their uncertainties.
Trial
Angular speed ω (rad/s)
Uncertainty in ω (rad/s)
Rotational kinetic energy K (J)
Uncertainty in K (J)
1
6.0
±0.2
0.44
±0.05
2
8.0
±0.2
0.78
±0.05
3
10.0
±0.2
1.21
±0.05
4
12.0
±0.2
1.70
±0.05
5
14.0
±0.2
2.26
±0.05
6
16.0
±0.2
2.90
±0.05
(1) Plot K on the vertical axis versus ω2 on the horizontal axis, including appropriate error bars for each data point.
(2) Determine the best-fit straight line for the plotted data and state its slope with its absolute uncertainty.
(3) From the slope, calculate the moment of inertia of the ring and the corresponding absolute uncertainty.
(4) The ring has a mass of 1.20kg and a radius of 0.22m. Calculate the theoretical moment of inertia for a thin ring and determine the percent error of the experimental value obtained in part (c).
(5) Identify one plausible systematic source of error in the experimental procedure that could account for any discrepancy between the experimental and theoretical moments of inertia, and explain its effect on the result.