---
title: "Reason: servo motor long, thin"
subject: "Electrical Machine"
chapter: 7
key: "semester_4/electrical_machine:servo-motor-long-small-diameter-reason"
source: https://www.bctengineer.com/q/semester_4/electrical_machine/servo-motor-long-small-diameter-reason
site: BCT Engineering
---

# Reason: servo motor long, thin

Electrical Machine · Chapter 7: Fractional Kilowatt Motors

- Asked in: 2071 Bhadra, 4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machine/servo-motor-long-small-diameter-reason
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-7

## Question

Give reason: Servo motor has longer length and smaller diameter compared to other normal motor.

## Short answer

For fast response, the torque-to-inertia ratio T/J ∝ 1/D² must be high. A small diameter rotor reduces inertia, while increased length maintains torque, giving high angular acceleration, quick starting and stopping, and precise control.

## Answer

A servo motor must respond very quickly to a changing control signal, so its **moment of inertia must be as small as possible** for the torque it develops.

- The angular acceleration of the rotor is α = T/J, where T is the developed torque and J is the moment of inertia. For fast acceleration and deceleration, T/J (torque-to-inertia ratio) must be large.
- For a cylindrical rotor of diameter D and length L: the torque developed varies approximately as D²L (since torque ∝ D × force, and force ∝ D·L), while the moment of inertia J ∝ D⁴L (mass ∝ D²L and radius² ∝ D²).
- So, T/J ∝ 1/D². Reducing the diameter D raises the ratio sharply, while the length L cancels out of the ratio. Length is therefore increased to get the required torque.
- Therefore a **long, small-diameter rotor** gives the highest torque per unit of inertia, short electromechanical time constant, quick starting, stopping and reversing, and less overshoot and hunting.
- This is why servo motors look long and thin compared to normal motors, whose rotors are short and wide to give power at lower cost.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What must a servo motor have for fast acceleration?
   A. A large moment of inertia
   B. A high ratio of torque to moment of inertia (alpha = T/J)
   C. A low torque
   D. A large diameter
   Answer: B. Angular acceleration is alpha = T/J, so the torque-to-inertia ratio must be large. (Key point: Torque-to-inertia ratio)

2. For a cylindrical rotor, how do torque and inertia scale?
   A. Torque is proportional to D^2 L and J is proportional to D^4 L
   B. Torque is proportional to D^4 L and J is proportional to D^2 L
   C. Both are proportional to D L
   D. Torque is proportional to L^2 and J to D
   Answer: A. Torque goes as D^2 L, while J goes as D^4 L, since mass is proportional to D^2 L and radius squared to D^2. (Key point: Scaling with D and L)

3. Since T/J is proportional to 1/D^2, what is done in design?
   A. Diameter is reduced and length increased to keep the required torque
   B. Diameter is increased and length reduced
   C. Both are increased
   D. Length is reduced to raise T/J
   Answer: A. Length cancels in T/J, so a small diameter raises the ratio and extra length provides the torque. (Key point: Effect of reducing diameter)

## Related in Electrical Machine

- [Servo motor length and diameter reason](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aservo-motor-long-small-diameter) — Electrical Machines, chapter 7

## Related in other subjects

- [Thin cylindrical shell: change in length and diameter](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Athin-cyl-shell-4m-25nmm2) — Strength of Materials, chapter 5