Table of Contents
Introduction
- Force is a key concept in physics. When applied to a rigid body, a force can cause only movement (motion). If force is applied to a non-rigid body, it can change both the shape/size and also cause movement.
- The mathematical definition of force is: Force = Rate of change of linear momentum. Simply, Force (F) = mass (m) × acceleration (a). This equation (F = ma) is basic for understanding force.
- Force is a vector quantity (it has direction). Its SI unit is Newton (N). There is also another unit called kilogram-force (kgf), where 1 kgf = 9.8 N (with g being acceleration due to gravity).
- In the syllabus, you will learn about moment of a force (turning effect), equilibrium, centre of gravity, and uniform circular motion. These topics use force in different ways, showing how force is everywhere in daily life—from opening doors to riding a bicycle.
- Force (बल) एक बहुत important concept है Physics में। जब हम rigid body (जो shape नहीं बदलती) पर force लगाते हैं, तो सिर्फ motion (movement) होता है। लेकिन non-rigid body पर force लगाने से उसका shape या size भी बदल सकता है।
- Force की mathematical definition है: Force = Linear Momentum का rate of change। आसान भाषा में, Force (F) = mass (m) × acceleration (a)। ये formula F = ma बार-बार आता है।
- Force एक vector quantity है, मतलब direction भी matter करती है। Force की SI unit है Newton (N)। और एक unit है kilogram-force (kgf), जिसमें 1 kgf = 9.8 N (ग्रहण acceleration due to gravity के साथ)।
- इस syllabus में आप पढ़ेंगे: Moment of Force (turning effect), Equilibrium (संतुलन), Centre of Gravity (गुरुत्व केंद्र), और Uniform Circular Motion। सारे topics में force अलग-अलग तरह से use होती है, जैसे दरवाज़ा खोलना या bicycle चलाना।
(A) MOMENT OF A FORCE AND EQUILIBRIUM
Translational and Rotational Motions
(1) Linear or Translational Motion
- Translational motion (also called linear motion) happens when a force causes a body to move from one place to another in a straight line or along a path, without spinning or rotating.
- In this type of motion, every part of the body moves the same distance and in the same direction, with no change in orientation. For example, when a ball is pushed and starts rolling straight, it shows translational motion.
- Translational motion यानी सीधी या linear motion होती है, जब force लगने पर कोई body एक जगह से दूसरी जगह जाती है, बिना घुमे या rotate हुए।
- इसमें body के सारे हिस्से equal distance और same direction में move करते हैं, orientation नहीं बदलती। जैसे, सीधी सड़क पर चलती car या ball का आगे-पीछे जाना।
(2) Rotational Motion
- Rotational motion happens when a body spins or turns around a fixed point or axis, due to a force applied at some distance from that point.
- In rotational motion, the body does not move from one place to another. Instead, it rotates about the pivot point. For example, when a door is pushed at its edge, it rotates around the hinges.
- Rotational motion यानी घूर्णन गति होती है, जब force लगने पर कोई body किसी fixed axis या point के चारों तरफ घूमती है।
- इसमें body अपनी जगह नहीं बदलती, बल्कि किसी pivot या axis के चारों तरफ rotate करती है। जैसे दरवाज़ा handle पर force लगाने से hinges के चारों तरफ घूमना।
Moment of a Force (Turning Effect of Force) or Torque
- The moment of a force (also called torque) is the turning effect produced when a force is applied to a body at some distance from a fixed point (called the pivot or fulcrum).
- Moment of force या जिसे torque भी कहते हैं, जब force किसी body पर लगाए और वह body एक fixed point (जिसे pivot या fulcrum कहते हैं) के चारों तरफ घूमने लगे, तो उस force का जो turning effect होता है, उसे moment of force कहते हैं।
- This turning effect causes the body to rotate or turn about the pivot. If a force is applied on a door handle, it rotates the door around its hinges due to the moment of force.
- जैसे दरवाज़े के hinges होते हैं pivot, और उसके handle पर force लगाने से door घूमता है। ये घुमाने वाला प्रभाव moment कहलाता है।
- The moment of force depends on these two main factors:
- The magnitude of the force applied.
- The perpendicular distance from the pivot to the line of action of the force.
- Moment of force पर दो चीजें असर करती हैं:
- लगाई गई force का size या मात्रा (magnitude)
- Pivot से force की perpendicular distance (फोर्स की line of action से pivot तक सबसे छोटा distance)
- Formula :
Moment of force = Force×Perpendicular distance
Moment of force = Force × Perpendicular distance or M = F×d ; M = F × d - Units:
The SI unit of moment of force is Newton-meter (Nm). - Clockwise and Anticlockwise moments:
- If the turning effect tends to rotate the body clockwise, the moment is taken negative.
- If the turning effect tends to rotate the body anticlockwise, the moment is taken positive.
- घड़ी की दिशा (clockwise) और उल्टी दिशा (anticlockwise) के moment:
- जब force से body घड़ी की दिशा में घूमे, तो moment Negative माना जाता है।
- जब body anti-clockwise घूमे, तो moment Positive माना जाता है।
- Common examples of moment of force:
- Opening or closing a door by pushing at the handle (far from hinges). (Door खोलने या बंद करने के लिए handle पर force लगाना।)
- Turning the steering wheel of a car by applying force at its rim. ( कार के steering wheel को rim पर force लगाकर घुमाना।)
- Pedaling a bicycle by pushing foot pedals far from the wheel’s center. ( साइकिल के pedals पर foot से force लगाना।)
- Using a spanner (wrench) to tighten or loosen a nut by applying force at the long handle. (Spanner से nut tight या loose करना।)
- Rotating the upper stone of a hand flour grinder by pushing the handle near its rim (maximum distance). ( हाथ से चलने वाले चक्की के ऊपर के पत्थर को उसके handle से घुमाना।)
- Conclusion:
The turning effect on a body depends not just on the size of the force but also on how far the force is applied from the pivot. More the perpendicular distance, less force is needed to produce the same turning effect or moment. This is why door handles, spanners, and bicycle pedals are placed far from the pivot or center. - निष्कर्ष:
किसी body को घुमाने में force की मात्रा और force का pivot से दूर होना दोनों महत्त्वपूर्ण होते हैं। ज़्यादा distance होने पर कम force से भी उतना ही turning effect मिलेगा। इसलिए door handles, spanner के long handles, और bicycle के pedals बड़े होते हैं।
Couple
What is a Couple?
- A couple is a pair of two equal and opposite forces acting parallel to each other but not along the same line. Because their lines of action do not coincide, the forces tend to rotate or turn the body without causing any translational (linear) movement.
- The resultant force of a couple is zero, meaning it does not move the body from place to place but only makes it rotate.
- A couple produces pure rotational motion (turning effect) on the body.
Couple क्या होता है?
- Couple दो ऐसे बराबर (equal) और उल्टे (opposite) forces होते हैं जो parallel रहते हुए, एक ही line में नहीं होते। क्योंकि इनके action lines अलग-अलग होती हैं, ये शरीर को घुमाने या मोड़ने का काम करते हैं बिना शरीर को हिलाए (translational motion नहीं होती)।
- Couple का total force zero होता है, इसलिए ये body को सीधे movement नहीं कराता, बस घुमाता है।
- Couple pure rotational motion (movement) पैदा करता है।
Examples of Couple ( Couple के उदाहरण )
- Turning the steering wheel of a car with both hands applying equal and opposite forces.
- कार के steering wheel को दोनों हाथों से घुमाना।
- Opening or closing a water tap where the forces by hands form a couple.
- Water tap को खोलना या बंद करना।
- Turning a key in a lock or winding an alarm clock key.
- Lock की चाबी या alarm clock की चाबी घुमाना।
- Using a screwdriver to rotate a screw.
- Screwdriver से screw को घुमाना।
- Opening or closing the cap of a bottle.
Moment of a Couple (Turning Effect of a Couple)
- The moment of a couple is the torque or the turning effect produced by the couple.
- It depends on:
- The magnitude of one of the forces FF (both are equal).
- The perpendicular distance dd between the two forces (called the couple arm).
- The formula for the moment of couple:Moment of couple=F×dMoment of couple=F×d
- Derivation:
Consider two forces F and −F acting at points A and B respectively, separated by a perpendicular distance d. Since the forces are equal and opposite, they produce rotation but no translation.
The total moment about any point is : M=F×dM = F×d This moment M causes rotation.
Moment of Couple (Couple के घुमाने का असर)
- Couple का moment वह torque है जो couple पैदा करता है।
- ये निर्भर करता है :
- एक force F की मात्रा (जो दोनों forces की बराबर होती है)।
- forces के बीच का perpendicular distance d (जिसे couple arm कहते हैं)।
- फॉर्मूला : Moment of couple = F×d ; Moment of couple = F×d
- Derivation (समझना):
मानिए दो forces F और −F हैं जो points A और B पर लगा है और इनके बीच perpendicular distance d है। ये forces शरीर को घुमाते हैं, लेकिन उसे सीधा नहीं हिलाते।
कुल moment होगा ; M = F×d यह torque शरीर को घुमाने के लिए काम करता है।
Summary
- A couple always produces rotation (pure turning effect).
- Couple हमेशा घुमाने वाला प्रभाव (pure rotation) पैदा करता है।
- The moment of the couple is force multiplied by the perpendicular distance between the forces.
- Couple का moment force और उनके बीच के perpendicular distance के Multiplication के बराबर होता है।
- The forces in a couple do not cancel the turning effect; they add to produce the rotation.
- Couple में forces एक-दूसरे का translational effect cancel कर देते हैं, लेकिन rotational effect जोड़ते हैं।
Equilibrium of Bodies
Equilibrium of Bodies can be clarified as :-
- Equilibrium means a state where all forces (and moments) acting on a body balance each other, so the body does not start moving or changing its motion.
- When a body is in equilibrium, either it stays at rest or moves with constant velocity; there is no acceleration.
Kinds of Equilibrium
- Static Equilibrium:
- Dynamic Equilibrium:
- The body moves at a constant velocity; again, all forces and torques balance, so speed and direction don’t change.
- Examples: A car driving with uniform (unchanging) speed, an object falling at terminal velocity, an airplane flying straight at constant height.
- Here, net force and net moment are both zero, but motion continues at steady rate.
Conditions for Equilibrium
A body is in equilibrium if both these are true:
- The resultant of all forces acting on it is zero (no unbalanced force).
- The algebraic sum of the moments (torques) of all forces about any point is zero (no unbalanced turning effect).
संतुलन (Equilibrium) और इसके प्रकार :-
- Equilibrium का मतलब है ऐसी स्थिति जिसमें body पर लगने वाले सारे forces और moments (torques) आपस में balance हो जाएं, जिससे body हिलती नहीं या अगर motion में है तो उसकी गति (velocity) constant रहती है।
- जब body equilibrium में है तब या तो पूरी तरह से rest पर रहती है या फिर smoothly constant velocity से चलती है।
Equilibrium के प्रकार (Kinds)
- Static Equilibrium:
- Dynamic Equilibrium:
- Body constant velocity से move करती है, पर सारे forces और moments फिर भी balance होते हैं।
- उदाहरण : Constant speed से चलती हुई car, पानी में गिरती हुई वस्तु जो terminal velocity पर पहुंच गई है, एक plane जो constant height पर सीधा उड़ रहा है।
- यहाँ भी net force और net moment दोनों zero हैं, movement steady रहती है।
Equilibrium की शर्तें (Conditions)
एक body तभी equilibrium में होती है :
- जब सारे forces का resultant zero हो ( कोई भी unbalanced force न हो )।
- जब सब forces के moments (torques) का algebraic sum zero हो ( कोई भी unbalanced turning effect न हो )।
Principle of Moments
- The Principle of Moments states :
For a body that is balanced (in equilibrium), the sum of all clockwise moments about a pivot equals the sum of all anticlockwise moments about the same pivot or point. - A moment is the turning effect produced by a force, calculated by multiplying the force with its perpendicular distance from the pivot (Moment = Force × Distance).
- In equation form : Sum of clockwise moments = Sum of anticlockwise moments Sum of clockwise moments = Sum of anticlockwise moments
or
F1×d1+ F2×d2 = F3×d3 + F4×d4 (where F is force, d is perpendicular distance from the pivot).
Verification of the Principle of Moments
- The principle of moments can be experimentally verified using a simple metre rule (as a beam), suspended from a point (pivot), with weights attached to each side.
- Adjust weights and positions so the beam is horizontal (balanced).
- The force by each weight creates a moment.
- If the beam is balanced:
- The moment caused by weights on one side clockwise equals the moment caused by weights on the other side anticlockwise.
- Example : If one weight of 1 N is placed 40 cm from the pivot on the left and another weight of 2 N is placed 20 cm from the pivot on the right :
Clockwise moment = 2N × 20cm = 40N cm
Anticlockwise moment =1N×40cm = 40N cm
So the rule is balanced, verifying the principle.
- Principle of Moments (मॉमेंट का सिद्धांत) कहता है :
जब कोई body equilibrium (संतुलन) में हो, तो pivot के बारे में सभी clockwise moments का योग सभी anticlockwise moments के योग के बराबर होता है। - Moment किसी force की turning effect है, जो force के और pivot के बीच की perpendicular distance से आती है (Moment = Force × Distance)।
- Equation में : Clockwise moments का योग = Anticlockwise moments का योग Clockwise moments का योग = Anticlockwise moments का योगया
F1×d1+F2×d2 = F3×d3+F4×d4 (जहाँ FF है force, dd है perpendicular distance pivot से)।
Principle of Moments की Verification
- Principle को verify करने के लिए एक simple experiment करते हैं। एक metre rule (beam) को एक fixed point (pivot) पर suspend करते हैं, और दोनों sides पर अलग-अलग weights लगाते हैं।
- Weights और positions को adjust करते हैं, जब beam horizontal (balanced) हो जाती है।
- एक-एक side पर weight लगाकर moments निकालते हैं (Moment = force × distance)।
- जब दोनों sides के moments बराबर होते हैं (एक side का clockwise और दूसरे का anticlockwise moment), तो beam balance रहती है।
- उदाहरण : अगर एक weight 1 N है 40 cm pivot से (बाएँ), दूसरा weight 2 N है 20 cm pivot से (दाएँ) : Clockwise moment =2 N×20 cm = 40 N cm
Anticlockwise moment =1 N×40 cm=40 N cm
दोनों बराबर, मतलब principle verify हो गया।
Solved Examples
- A body is pivoted at a point. A force of 10 N is applied at a distance of 30 cm from the pivot. Calculate the moment of force about the pivot.
Ans : F = 10 N , r = 30 cm = 0.3 m
Moment of Force = \(F \times r\)
Moment of Force = \(10 \times 0.3\) = 3 Nm
- The moment of a force of 5 N about a point P is 2 N m. Calculate the distance of point of application of the force from the point P.
Ans : Given, moment of force = 2 N m, F = 5 N
If the distance of a point of application of force from the point P is r metre, then
Moment of force = \(force \times distance\)
2 = \(5 \times r\)
r = \(\frac{2}{5}\) = 0.4 m
Exercise 1A
1. State the condition when on applying a force, the body has: (a) the translational motion, (b) the rotational motion.
(a) Translational motion: Body should be free to move; force will push or pull it straight.
(b) Rotational motion: Body should be pivoted at a fixed point; force will make the body rotate about that axis.
2. Define moment of force and state its S.I. unit.
- Moment of force: Turning effect produced by a force about a point or axis.
- Definition: Product of force and the perpendicular distance from axis.
- S.I. unit: Newton metre (N m).
3. State whether the moment of force is a scalar or vector quantity.
4. State two factors affecting the turning effect of a force.
5. When does a body rotate? State one way to change the direction of rotation of the body. Give a suitable example.
- Body rotates: When a force is applied at a distance from the pivot.
- Direction can be changed: By changing the point of application or direction of force.
- Example: Door opens anticlockwise if pushed at handle, clockwise if pulled from opposite side.
6. Write the expression for the moment of force about a given axis.
Moment of force=Force×Perpendicular distance from axisMoment of force=Force×Perpendicular distance from axis
7. State one way to reduce the moment of a given force about a given axis.
Reduce the perpendicular distance between axis and line of force.
8. State one way to obtain a greater moment of a force about a given axis.
Increase the perpendicular distance from axis; use a longer handle.
9. What do you understand by clockwise and anticlockwise moment of force? When is it taken positive?
- Clockwise moment: Turns body in “clockwise” direction, taken as negative.
- Anticlockwise moment: Turns body in opposite direction, taken as positive.
10. Why is it easier to open a door by applying the force at the free end of it?
- Farther from hinges (pivot), distance is maximum, so less force needed for same turning effect (moment).
11. The stone of a hand flour grinder is provided with a handle near its rim. Give reason.
12. It is easier to turn the steering wheel of a large diameter than that of a small diameter. Give reason.
13. A spanner (or wrench) has a long handle. Why?
14. A, B and C are the three forces each of magnitude 4 N acting in the plane of paper as shown in Fig. 1.25. The point O lies in the same plane. Which force has least moment about O? Which has greatest? Name forces producing clockwise & anticlockwise moment. What is resultant torque?
Least moment: Force nearest to O (C)
Greatest: Farthest from O (A)
Clockwise moment: Forces A & B
Anticlockwise moment: Force C
Resultant torque: Given by directions and distances in diagram.
15. The adjacent diagram shows a heavy roller, with its axle at O, which is to be raised on pavement XY by applying a minimum possible force. Show by an arrow on the diagram the point of application and direction of force to be applied.
- Point of application: At edge farthest from pavement
- Direction: Upwards and tangential to roller surface.
16. A body is acted upon by two forces each of magnitude F, but in opposite directions. State the effect if (a) both at same point, (b) at two different points at separation r.
(a) Forces cancel – no rotation, no translation
(b) They act as a couple and rotate the body about middle point.
17. Draw a neat labelled diagram to show the direction of two forces acting on a body to produce rotation in it. Also mark the point O about which the rotation takes place.
- Diagram should show a lever/bar with forces at ends, arrows showing direction, and point O as pivot.
18. What do you understand by the term couple? State its effect. Give two examples of couple in daily life.
- Couple: Two equal, opposite, parallel forces not acting at same line.
- Effect: Produces rotation without translation
- Examples: Turning steering wheel, loosening nut with spanner.
19. Define moment of couple. Write its S.I. unit.
20. Prove that Moment of couple = Force × couple arm.
- Each force (FF) produces moment (F×aF×a), total moment is sum, so F×a+F×a=F×2aF×a+F×a=F×2a (if arm is 2a2a), thus general: Moment = Force × couple arm.
21. What do you mean by equilibrium of a body? State the condition when a body is in (i) static, (ii) dynamic, equilibrium. Give one example each.
- Equilibrium: No change in motion, rotation or shape.
- (i) Static: Body at rest, e.g., book on table
- (ii) Dynamic: Body moving with constant speed, e.g., car at steady velocity
22. State two conditions for a body acted upon by several forces to be in equilibrium.
23. State the principle of moments. Give one device as application.
- Principle: Sum of anticlockwise moments = sum of clockwise moments in equilibrium.
- Application: Beam balance.
24. Describe a simple experiment to verify the principle of moments with a metre rule, fulcrum, two springs and weights.
- Suspend a metre rule horizontally from a support at centre (O). Hang weights at variable points right/left. Adjust positions until rule stays horizontal; then moments (weight × distance) on one side equals on the other.
25. Complete the following sentences:
(i) The S.I. unit of moment of force is N m
(ii) In equilibrium, algebraic sum of moments of all forces about point of rotation is zero
(iii) In a beam balance, when the beam is balanced in horizontal position, it is in static equilibrium
(iv) The moon revolving around the earth is in dynamic equilibrium.
(B) CENTRE OF GRAVITY
Centre of Gravity: Definition and Concept
- The centre of gravity (CG) of a body is the point at which the whole weight of the body can be considered to act, no matter how the body is oriented.
- For all practical purposes, the weight of the entire body acts at this single point.
- If the body is freely supported at its centre of gravity, it will balance perfectly and remain in equilibrium.
- The centre of gravity (CG) is that special point in a body जहां पूरे body का weight act करता है, चाहे body कैसे भी रखी हो।
- Body को अपने centre of gravity पर support करने से body perfectly balance रहती है।
- Example: Ruler को उसके बीच में ही finger पर रखो, वही उसका centre of gravity है।
Examples and Explanation
- Seesaw: The board is balanced when the centre of gravity is directly above the pivot.
- Balancing a ruler: A uniform ruler balances on a fingertip at its centre—this point is the centre of gravity.
- Hanging a plumb bob: The centre of gravity lies directly below the point of suspension.
- Ring or hollow sphere: Centre of gravity may lie at a point with no material, such as at the centre of a ring.
- See-saw: बच्चों का see-saw तभी balance होता है जब दोनों sides का combined weight centre of gravity के ऊपर हो।
- Flat Ring: Ring का centre of gravity उसके geometric centre में होता है, भले ही वहां कोई matter न हो।
- Uniform Ruler: Uniform ruler अपने 50 cm mark (बीच) पर balance हो जाता है, वही उसका centre of gravity है।
- Suspended Object: Body को कहीं से लटकाओ (suspend करो), वह ऐसे रूकेगी कि उसका centre of gravity suspension point के ठीक नीचे होगा।
Centre of Gravity of Some Regular Objects
Here’s where the centre of gravity is found for common regular shapes:
| Object | Centre of Gravity Position |
|---|---|
| Uniform rod | Midpoint of the rod |
| Circular disc | Geometric centre of the disc |
| Solid/hollow sphere | Centre of the sphere |
| Circular ring | Geometric centre of the ring |
| Cylinder (solid/hollow) | Midpoint on its axis |
| Solid cone | Height h/4h/4 above the base on axis |
| Hollow cone | Height h/3h/3 above the base on axis |
| Triangular lamina | Intersection point of medians |
| Rectangle/parallelogram/square | Intersection point of the diagonals |
- The centre of gravity depends on the distribution of mass and can change if the body’s shape changes.
| Object | Centre of Gravity Location |
|---|---|
| Uniform Rod | Mid-point |
| Circular Disc | Geometric centre |
| Solid या Hollow Sphere | Geometric centre |
| Circular Ring | Centre (जहां कोई mass नहीं) |
| Cylinder | Axis का mid-point |
| Solid Cone | Axis पर base से h/4 ऊपर |
| Hollow Cone | Axis पर base से h/3 ऊपर |
| Triangle Lamina (त्रिभुज) | Medians के intersection पर |
| Rectangle/Square/Parallelogram | Diagonals के intersection पर |
- Centre of gravity body की shape या mass distribution पर depend करता है।
- कभी-कभी यह point body के अंदर नहीं भी हो सकता, जैसे hollow sphere या ring।
Centre of Gravity and the Balance Point
- A body will balance at its centre of gravity.
- For example, a metre rule will balance on a knife edge or finger exactly under its centre of gravity (the 50 cm mark for a uniform rule).
- The centre of gravity for a uniform square or lamina can be tested by balancing on the tip of a nail—whenever the CG is directly above the support, the body balances.
- Solid body को centre of gravity पे support करो, तो body खुद balance में रहती है।
- Example: Uniform metre rule उसकी exact middle (50 cm) पे knife edge या finger पे balance हो जाता है — यही उसका centre of gravity है।
- Square या lamina को nail के tip पर भी balance किया जा सकता है।
Determination of Centre of Gravity of an Irregular Lamina (Plumb Line Method)
For objects with irregular shapes, the centre of gravity can be found by experiment:
- Make holes: Punch three small holes near the edge of the lamina (labeled A, B, C).
- Suspend from a hole: Hang the lamina from hole A on a pin. It will come to rest with the centre of gravity vertically below the point of suspension.
- Hang a plumb line: Hang a plumb line (a string with a small weight) from the same point. When at rest, draw a straight line along the plumb line on the lamina.
- Repeat: Suspend the lamina from hole B, hang the plumb line, and draw the new vertical line.
- Again: Repeat for hole C.
- Find the intersection: The point where all three lines cross is the centre of gravity (CG) of the irregular lamina.
Irregular Lamina – Plumb Line Method (अनियमित आकार की पट्टी के लिए प्रयोग)
Irregular जो shape होती है, उसका centre of gravity कैसे निकालें? Plumb line experiment से:
- Lamina में किनारे पे तीन छेद कर दो (a, b, c)।
- Hole a से lamina को pin पर suspend करो। साथ में plumb line (string + weight) भी वही से लटका दो।
- Lamina जब still हो जाए, plumb line के साथ एक सीधी line draw करो।
- यही काम दुबारा hole b और फिर hole c से repeat करो।
- Plumb line की तीनों lines जहां meet करेंगी, वही point है centre of gravity (G)
Summary points:
- The centre of gravity may be within or outside the material of the body.
- For regular shapes, it can be found by geometry; for irregular shapes, experimental methods like the plumb line are used.
- At the centre of gravity, the object is perfectly balanced and the total turning effect (moment) of the weight on all sides cancels out.
- Centre of gravity body के अंदर, surface पर, या बाहर भी हो सकता है
- Regular shapes में, geometry से पता चलता है; irregular में, प्रयोग से।
- जिस point पर centre of gravity है, वहाँ object perfectly balance रहेगा, moments दोनों sides cancel हो जाते हैं।