---
title: "An experiment is conducted to determine the unknown rotational inertia \\(I\\) of an irregularly shaped rotor mounted on a fixed horizontal axle.  A light string is wrapped around a cylindrical hub of radius \\(r\\) fixed coaxially to the rotor, and a block of mass \\(m\\) is suspended from the free end. The block is released from rest and descends with a constant downward acceleration \\(a\\), and the student calculates \\(I\\) from the measured acceleration using the frictionless model \\(I = m r^2 \\left(\\dfrac{g}{a} – 1\\right)\\).  If the axle bearings exert an unmodeled, constant frictional torque \\(\\tau_f\\) that opposes rotation, how does the student’s calculated rotational inertia compare to the true rotational inertia of the rotor, and what is the physical justification?"
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url: "https://nerd-notes.com/ubq/124245/"
date_modified: "2026-09-28T14:04:29+00:00"
---

# An experiment is conducted to determine the unknown rotational inertia \(I\) of an irregularly shaped rotor mounted on a fixed horizontal axle.

A light string is wrapped around a cylindrical hub of radius \(r\) fixed coaxially to the rotor, and a block of mass \(m\) is suspended from the free end. The block is released from rest and descends with a constant downward acceleration \(a\), and the student calculates \(I\) from the measured acceleration using the frictionless model \(I = m r^2 \left(\dfrac{g}{a} – 1\right)\).

If the axle bearings exert an unmodeled, constant frictional torque \(\tau_f\) that opposes rotation, how does the student’s calculated rotational inertia compare to the true rotational inertia of the rotor, and what is the physical justification?

An experiment is conducted to determine the unknown rotational inertia \(I\) of an irregularly shaped rotor mounted on a fixed horizontal axle.

A light string is wrapped around a cylindrical hub of radius \(r\) fixed coaxially to the rotor, and a block of mass \(m\) is suspended from the free end. The block is released from rest and descends with a constant downward acceleration \(a\), and the student calculates \(I\) from the measured acceleration using the frictionless model \(I = m r^2 \left(\dfrac{g}{a} - 1\right)\).

If the axle bearings exert an unmodeled, constant frictional torque \(\tau_f\) that opposes rotation, how does the student's calculated rotational inertia compare to the true rotational inertia of the rotor, and what is the physical justification?

![A front-view schematic of a rotational dynamics apparatus. At the center is a fixed horizontal axle represented by a small filled circle. Mounted on the axle is an irregularly shaped planar rotor with a smooth, closed, asymmetrical curved boundary. Concentric with the axle is a smaller circular hub of radius \(r\), shown with a dashed radial segment labeled \(r\). A vertical line representing a light string tangentially leaves the right edge of the circular hub and extends straight downward. Suspended from the bottom end of the string is a rectangular block labeled \(m\). A straight downward arrow next to the block indicates the direction of motion. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604268-NjZJT5.jpg)

- **A.** The calculated rotational inertia is greater than the true rotational inertia because the bearing friction reduces the downward acceleration of the block, causing the rotor to appear more resistant to rotational acceleration.
- **B.** The calculated rotational inertia is greater than the true rotational inertia because the bearing friction reduces the tension in the string, which increases the net downward force accelerating the hanging block.
- **C.** The calculated rotational inertia is less than the true rotational inertia because the bearing friction reduces the net torque acting on the rotor, leading to an underestimation of the rotor's rotational inertia.
- **D.** The calculated rotational inertia is less than the true rotational inertia because mechanical energy is dissipated by friction, resulting in a lower final angular speed than predicted by the frictionless model.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124245/*