---
title: "Servo motor length and diameter reason"
subject: "Electrical Machines"
chapter: 7
key: "semester_4/electrical_machines:servo-motor-long-small-diameter"
source: https://www.bctengineer.com/q/semester_4/electrical_machines/servo-motor-long-small-diameter
site: BCT Engineering
---

# Servo motor length and diameter reason

Electrical Machines · 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_machines/servo-motor-long-small-diameter
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-7

## Question

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

## Short answer

To achieve fast response, torque depends on D²L while inertia depends on D⁴L. Reducing diameter drastically lowers inertia, and increasing length maintains torque, giving a high torque-to-inertia ratio for rapid acceleration, deceleration, and reversal.

## Answer

A servo motor is used in control systems that need a **fast response** to the error signal, such as starting, stopping and reversing in a very short time. This requires a high torque-to-inertia ratio, i.e. a small mechanical time constant.

1. **Torque produced** is proportional to the volume of the rotor: $T \propto D^2 L$ (D = diameter, L = length). So the required torque can be obtained with a long rotor instead of a wide one.
2. **Moment of inertia** of a rotor is $J \propto D^4 L$. The inertia depends on the fourth power of the diameter but only linearly on the length.
3. So reducing the diameter lowers the inertia drastically, while the torque is maintained by increasing the length. The torque-to-inertia ratio $\propto \frac{1}{D^2}$, which increases as $D$ is made smaller.
4. A low-inertia rotor accelerates and decelerates quickly, so the motor follows the control signal accurately with little overshoot. The small diameter also means the rotor stores little kinetic energy, which makes quick reversal possible.

Hence the servo motor is built long and thin, unlike normal motors, which are designed for efficiency and economy rather than speed of response.

## Check yourself

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

1. Why does a servo motor need a high torque-to-inertia ratio?
   A. So it can start, stop and reverse quickly in response to the error signal
   B. So it can run at maximum efficiency at rated load
   C. So it can be built cheaply
   D. So it can store more rotational energy
   Answer: A. Servo motors are used in control systems needing fast response; a high torque-to-inertia ratio (small mechanical time constant) gives quick starting, stopping and reversing. (Key point: Need for fast response)

2. According to the answer, how does the torque of the rotor depend on diameter D and length L?
   A. T is proportional to D^4 L
   B. T is proportional to D^2 L, i.e. rotor volume
   C. T is proportional to D L^2
   D. T is proportional to L only
   Answer: B. Torque is proportional to rotor volume, T ~ D^2 L, so the torque lost by a smaller diameter can be made up by extra length. (Key point: Torque dependence on dimensions)

3. How does the moment of inertia of the rotor vary with D and L?
   A. J ~ D^2 L
   B. J ~ D L^4
   C. J ~ D^4 L
   D. J ~ D^2 L^2
   Answer: C. Inertia goes as the fourth power of diameter but only linearly with length, so reducing D cuts inertia drastically. (Key point: Inertia dependence on dimensions)

4. Why is the servo rotor made long and thin?
   A. Torque to inertia ratio is proportional to D, so a larger D is better
   B. Reducing D lowers inertia strongly while torque is kept by increasing L, raising the ratio (proportional to 1/D^2)
   C. Increasing L reduces both torque and inertia equally
   D. A thin rotor increases efficiency and economy
   Answer: B. T/J ~ 1/D^2, so a small D gives a high ratio; the torque lost is recovered by increasing length. (Key point: Torque-to-inertia ratio)

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## Related in other subjects

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