- 2071 Bhadra · 4 marks
Reason: servo motor long, thin
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.
Give reason: Servo motor has longer length and smaller diameter compared to other normal motor.
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.
✓ Answer checked by Claude Opus 5.5 (high effort)
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