---
title: "Static versus dynamic balancing"
subject: "Theory of Mechanism and Machine II"
chapter: 5
key: "semester_7/theory_of_mechanism_and_machine_ii:static-dynamic-balancing-differentiate"
source: https://www.bctengineer.com/q/semester_7/theory_of_mechanism_and_machine_ii/static-dynamic-balancing-differentiate
site: BCT Engineering
---

# Static versus dynamic balancing

Theory of Mechanism and Machine II · Chapter 5: Balance of Machinery

- Asked in: year not given, 5 marks
- Video: [The difference between Static and Dynamic Unbalance](https://www.youtube.com/watch?v=JB8i7LtY3mU) — Antalz
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/theory_of_mechanism_and_machine_ii/static-dynamic-balancing-differentiate
- Whole chapter: https://www.bctengineer.com/md/semester_7/theory_of_mechanism_and_machine_ii/chapter-5

## Question

Differentiate between static balancing and dynamic balancing of rotating masses. State the conditions for complete balance of several masses rotating in different planes.

## Short answer

Static balancing eliminates the resultant centrifugal force (Σmr=0) for coplanar masses; dynamic balancing also eliminates the resultant couple (Σmrl=0), requiring two correction planes. Dynamic balance ensures static balance, not conversely. Complete balance: vector sum of centrifugal forces = 0 and vector sum of couples about any plane = 0.

## Answer

Unbalanced rotating masses produce a centrifugal force $mr\omega^2$ that rotates with the shaft and loads the bearings. Balancing removes it.

#### Static vs dynamic balancing
| Point | Static balancing | Dynamic balancing |
|---|---|---|
| Condition satisfied | Resultant centrifugal force is zero | Resultant force and resultant couple are both zero |
| Masses | Can be in one plane or several planes | Masses in different planes |
| Test | Shaft placed on rails (knife edges); it stays at rest in any position | Needs a balancing machine with the shaft rotating |
| Planes needed | One correcting mass in one plane | At least two correcting planes |
| Remaining defect | A couple may remain | No residual force or couple |
| Suitable for | Narrow discs and wheels | Long rotors, crankshafts, armatures |

Dynamic balance includes static balance, but static balance does not guarantee dynamic balance.

#### Conditions for complete balance (several masses in different planes)
1. The vector sum of all the centrifugal forces is zero:
$$
\sum mr\omega^2 = 0 \;\Rightarrow\; \sum mr = 0
$$
2. The vector sum of the couples about any reference plane is zero:
$$
\sum mr\,l = 0
$$
where $l$ is the axial distance of each plane from the reference plane. Both conditions are solved graphically (force and couple polygons) or by resolving into horizontal and vertical components.

## Check yourself

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

1. Static balance only requires that:
   A. The resultant centrifugal force is zero
   B. Both force and couple are zero
   C. Only the couple is zero
   D. The masses are equal
   Answer: A. Static balance means vector sum of centrifugal forces is zero; a couple may remain. (Key point: Static balancing condition)

2. Which statement about dynamic balancing is right?
   A. Both resultant force and resultant couple are zero, and static balance follows
   B. It does not include static balance
   C. Static balance guarantees dynamic balance
   D. It needs only one correcting plane
   Answer: A. Dynamic balance includes static balance, but static balance does not guarantee it; it needs at least two correcting planes. (Key point: Dynamic balance)

3. A shaft is tested for static balance by:
   A. Placing it on knife-edge rails and seeing if it stays at rest in any position
   B. Spinning it on a balancing machine
   C. Measuring bearing temperature
   D. Weighing it
   Answer: A. A statically balanced shaft stays at rest in any position on rails. (Key point: Test method)

4. Complete balance of masses in different planes needs:
   A. Sum mr = 0 and sum mr l = 0
   B. Sum mr = 0 only
   C. Sum mr l = 0 only
   D. Sum m = 0 and sum l = 0
   Answer: A. Forces (sum mr) and couples about a reference plane (sum mr l) must both vanish. (Key point: Couple condition)

## Related in Theory of Mechanism and Machine II

- [Dynamic balancing with two correction planes](https://www.bctengineer.com/question.md?key=semester_7%2Ftheory_of_mechanism_and_machine_ii%3Abalancing-masses-two-planes-numerical) — Theory of Mechanism and Machine II, chapter 5
- [Balancing one mass using two planes](https://www.bctengineer.com/question.md?key=semester_7%2Ftheory_of_mechanism_and_machine_ii%3Asingle-mass-two-plane-balance-derivation) — Theory of Mechanism and Machine II, chapter 5
- [Balancing four masses in one plane](https://www.bctengineer.com/question.md?key=semester_7%2Ftheory_of_mechanism_and_machine_ii%3Abalancing-masses-same-plane-numerical) — Theory of Mechanism and Machine II, chapter 5

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